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Easy Evaluation of Streamer Discharge Criteria Göran1ABB AB, Corporate Research*Corresponding author: Abstract:devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission systems aprovided by a gas, e.g. air or SF Keywords: Streamer, Breakdown, Flashover 1. Introduction
transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e. tryingpossible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels smaller, while at the same time also these voltage differences, obviously makes the occurrence of electric discharges and flashoverssee Fig. 1,happen clearly requires a very thorough design work; critical areas suffering from excessive stress mustdesign modifications. Doing this by experiments is very timenumerical simulations of the electric field distribution provide a highly useful tool.Unfortunately, to translate the result from an into a statement whether a discharge or flashover will occur or not.
a discharge is the ionization of the insulating gas[1]ionization of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and attachment rates. strongly dependent on the electric field
depending on the gas.
Easy Evaluation of Streamer Discharge CriteriaGöranABB AB, Corporate Research
*Corresponding author:
Abstract:devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission systems aprovided by a gas, e.g. air or SF
Keywords: Streamer, Breakdown, Flashover
1. Introduction
In recent development of efficient power transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e. tryingpossible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels smaller, while at the same time also these voltage differences, obviously makes the occurrence of electric discharges and flashoverssee Fig. 1,happen clearly requires a very thorough design work; critical areas suffering from excessive stress mustdesign modifications. Doing this by experiments is very timenumerical simulations of the electric field distribution provide a highly useful tool.Unfortunately, to translate the result from an into a statement whether a discharge or flashover will occur or not.
The basic mechanism behind the creation of a discharge is the ionization of the insulating gas[1]. An important quantity ionization of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and attachment rates. strongly dependent on the electric field
eff (depending on the gas.
Easy Evaluation of Streamer Discharge CriteriaGöran ErikssonABB AB, Corporate Research
*Corresponding author:
Abstract:devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission systems aprovided by a gas, e.g. air or SF
Keywords: Streamer, Breakdown, Flashover
1. Introduction
In recent development of efficient power transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e. trying to make the equipment as small as possible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels smaller, while at the same time also these voltage differences, obviously makes the occurrence of electric discharges and flashoverssee Fig. 1,happen clearly requires a very thorough design work; critical areas suffering from excessive stress mustdesign modifications. Doing this by experiments is very timenumerical simulations of the electric field distribution provide a highly useful tool.Unfortunately, to translate the result from an into a statement whether a discharge or flashover will occur or not.
The basic mechanism behind the creation of a discharge is the ionization of the insulating gas
. An important quantity ionization of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and attachment rates. strongly dependent on the electric field
(E) and the shape of this function varies depending on the gas.
Easy Evaluation of Streamer Discharge CriteriaEriksson
ABB AB, Corporate Research*Corresponding author:
Abstract: devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission systems and components where provided by a gas, e.g. air or SF
Keywords: Streamer, Breakdown, Flashover
1. Introduction
In recent development of efficient power transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e.
to make the equipment as small as possible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels smaller, while at the same time also these voltage differences, obviously makes the occurrence of electric discharges and flashoverssee Fig. 1,happen clearly requires a very thorough design work; critical areas suffering from excessive stress must design modifications. Doing this by experiments is very timenumerical simulations of the electric field distribution provide a highly useful tool.Unfortunately, to translate the result from an into a statement whether a discharge or flashover will occur or not.
The basic mechanism behind the creation of a discharge is the ionization of the insulating gas
. An important quantity ionization of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and attachment rates. strongly dependent on the electric field
) and the shape of this function varies depending on the gas.
Easy Evaluation of Streamer Discharge CriteriaEriksson
ABB AB, Corporate Research*Corresponding author:
An easily implemented method is devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission
nd components where provided by a gas, e.g. air or SF
Keywords: High voltageStreamer, Breakdown, Flashover
1. Introduction
In recent development of efficient power transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e.
to make the equipment as small as possible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels smaller, while at the same time also these voltage differences, obviously makes the occurrence of electric discharges and flashoverssee Fig. 1, more probable. Avoiding this to happen clearly requires a very thorough design work; critical areas suffering from excessive
be identified followed by appropriate design modifications. Doing this by experiments is very time-consuming and expensive. Here, numerical simulations of the electric field distribution provide a highly useful tool.Unfortunately, to translate the result from an into a statement whether a discharge or flashover will occur or not.
The basic mechanism behind the creation of a discharge is the ionization of the insulating gas
. An important quantity eff, which is the rate of net production
of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and attachment rates. strongly dependent on the electric field
) and the shape of this function varies depending on the gas.
Easy Evaluation of Streamer Discharge CriteriaEriksson*1
ABB AB, Corporate Research*Corresponding author:
An easily implemented method is devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission
nd components where provided by a gas, e.g. air or SF
High voltageStreamer, Breakdown, Flashover
1. Introduction
In recent development of efficient power transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e.
to make the equipment as small as possible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels smaller, while at the same time also these voltage differences, obviously makes the occurrence of electric discharges and flashovers
more probable. Avoiding this to happen clearly requires a very thorough design work; critical areas suffering from excessive
be identified followed by appropriate design modifications. Doing this by experiments
consuming and expensive. Here, numerical simulations of the electric field distribution provide a highly useful tool.Unfortunately, however, to translate the result from an into a statement whether a discharge or flashover will occur or not.
The basic mechanism behind the creation of a discharge is the ionization of the insulating gas
. An important quantity , which is the rate of net production
of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and attachment rates. strongly dependent on the electric field
) and the shape of this function varies depending on the gas.
Easy Evaluation of Streamer Discharge Criteria1
ABB AB, Corporate Research*Corresponding author:
An easily implemented method is devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission
nd components where provided by a gas, e.g. air or SF
High voltageStreamer, Breakdown, Flashover
In recent development of efficient power transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e.
to make the equipment as small as possible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels smaller, while at the same time also these voltage differences, obviously makes the occurrence of electric discharges and flashovers
more probable. Avoiding this to happen clearly requires a very thorough design work; critical areas suffering from excessive
be identified followed by appropriate design modifications. Doing this by experiments
consuming and expensive. Here, numerical simulations of the electric field distribution provide a highly useful tool.
however, to translate the result from an into a statement whether a discharge or flashover
The basic mechanism behind the creation of
a discharge is the ionization of the insulating gas. An important quantity
, which is the rate of net production of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and attachment rates. Since the ionization rate is strongly dependent on the electric field
) and the shape of this function varies depending on the gas.
Easy Evaluation of Streamer Discharge Criteria
ABB AB, Corporate Research*Corresponding author: SE
An easily implemented method is devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission
nd components where provided by a gas, e.g. air or SF
High voltageStreamer, Breakdown, Flashover
In recent development of efficient power transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e.
to make the equipment as small as possible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels smaller, while at the same time also these voltage differences, obviously makes the occurrence of electric discharges and flashovers
more probable. Avoiding this to happen clearly requires a very thorough design work; critical areas suffering from excessive
be identified followed by appropriate design modifications. Doing this by experiments
consuming and expensive. Here, numerical simulations of the electric field distribution provide a highly useful tool.
however, to translate the result from an into a statement whether a discharge or flashover
The basic mechanism behind the creation of a discharge is the ionization of the insulating gas
. An important quantity , which is the rate of net production
of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and
Since the ionization rate is strongly dependent on the electric field
) and the shape of this function varies depending on the gas.
Easy Evaluation of Streamer Discharge Criteria
ABB AB, Corporate ResearchSE-721 78, Västerås, Sweden
An easily implemented method is devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission
nd components where provided by a gas, e.g. air or SF
High voltageStreamer, Breakdown, Flashover
In recent development of efficient power transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e.
to make the equipment as small as possible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels smaller, while at the same time also these voltage differences, obviously makes the occurrence of electric discharges and flashovers
more probable. Avoiding this to happen clearly requires a very thorough design work; critical areas suffering from excessive
be identified followed by appropriate design modifications. Doing this by experiments
consuming and expensive. Here, numerical simulations of the electric field distribution provide a highly useful tool.
however, it is not strato translate the result from an into a statement whether a discharge or flashover
The basic mechanism behind the creation of a discharge is the ionization of the insulating gas
. An important quantity , which is the rate of net production
of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and
Since the ionization rate is strongly dependent on the electric field
) and the shape of this function varies
Easy Evaluation of Streamer Discharge Criteria
ABB AB, Corporate Research721 78, Västerås, Sweden
An easily implemented method is devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission
nd components where provided by a gas, e.g. air or SF6
High voltage, Electric field, Streamer, Breakdown, Flashover
In recent development of efficient power transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e.
to make the equipment as small as possible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels smaller, while at the same time also these voltage differences, obviously makes the occurrence of electric discharges and flashovers
more probable. Avoiding this to happen clearly requires a very thorough design work; critical areas suffering from excessive
be identified followed by appropriate design modifications. Doing this by experiments
consuming and expensive. Here, numerical simulations of the electric field distribution provide a highly useful tool.
it is not strato translate the result from an Einto a statement whether a discharge or flashover
The basic mechanism behind the creation of a discharge is the ionization of the insulating gas
. An important quantity , which is the rate of net production
of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and
Since the ionization rate is strongly dependent on the electric field
) and the shape of this function varies
Easy Evaluation of Streamer Discharge Criteria
ABB AB, Corporate Research 721 78, Västerås, Sweden
An easily implemented method is devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission
nd components where the insulation is 6.
, Electric field, Streamer, Breakdown, Flashover.
In recent development of efficient power transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e.
to make the equipment as small as possible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels smaller, while at the same time also these voltage differences, obviously makes the occurrence of electric discharges and flashovers
more probable. Avoiding this to happen clearly requires a very thorough design work; critical areas suffering from excessive
be identified followed by appropriate design modifications. Doing this by experiments
consuming and expensive. Here, numerical simulations of the electric field distribution provide a highly useful tool.
it is not straE-field calculation
into a statement whether a discharge or flashover
The basic mechanism behind the creation of a discharge is the ionization of the insulating gas
. An important quantity is the effective , which is the rate of net production
of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and
Since the ionization rate is strongly dependent on the electric field
) and the shape of this function varies
Easy Evaluation of Streamer Discharge Criteria
721 78, Västerås, Sweden
An easily implemented method is devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission
the insulation is
, Electric field,
In recent development of efficient power transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e.
to make the equipment as small as possible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels smaller, while at the same time also these voltage differences, obviously makes the occurrence of electric discharges and flashovers
more probable. Avoiding this to happen clearly requires a very thorough design work; critical areas suffering from excessive
be identified followed by appropriate design modifications. Doing this by experiments
consuming and expensive. Here, numerical simulations of the electric field distribution provide a highly useful tool.
it is not straightforward field calculation
into a statement whether a discharge or flashover
The basic mechanism behind the creation of a discharge is the ionization of the insulating gas
is the effective , which is the rate of net production
of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and
Since the ionization rate is strongly dependent on the electric field
) and the shape of this function varies
Easy Evaluation of Streamer Discharge Criteria
721 78, Västerås, Sweden
An easily implemented method is devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission
the insulation is
, Electric field,
In recent development of efficient power transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e.
to make the equipment as small as possible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels smaller, while at the same time also increasing these voltage differences, obviously makes the occurrence of electric discharges and flashovers
more probable. Avoiding this to happen clearly requires a very thorough design work; critical areas suffering from excessive
be identified followed by appropriate design modifications. Doing this by experiments
consuming and expensive. Here, numerical simulations of the electric field distribution provide a highly useful tool.
ightforward field calculation
into a statement whether a discharge or flashover
The basic mechanism behind the creation of a discharge is the ionization of the insulating gas
is the effective , which is the rate of net production
of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and
Since the ionization rate is strongly dependent on the electric field E
) and the shape of this function varies
Easy Evaluation of Streamer Discharge Criteria
721 78, Västerås, Sweden
An easily implemented method is devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission
the insulation is
, Electric field,
In recent development of efficient power transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e.
to make the equipment as small as possible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels
increasing these voltage differences, obviously makes the occurrence of electric discharges and flashovers
more probable. Avoiding this to happen clearly requires a very thorough design work; critical areas suffering from excessive
be identified followed by appropriate design modifications. Doing this by experiments
consuming and expensive. Here, numerical simulations of the electric field distribution provide a highly useful tool.
ightforward field calculation
into a statement whether a discharge or flashover
The basic mechanism behind the creation of a discharge is the ionization of the insulating gas
is the effective , which is the rate of net production
of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and
Since the ionization rate is E, so is
) and the shape of this function varies
Easy Evaluation of Streamer Discharge Criteria
721 78, Västerås, Sweden
An easily implemented method is devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission
the insulation is
, Electric field,
In recent development of efficient power transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e.
to make the equipment as small as possible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels
increasing these voltage differences, obviously makes the occurrence of electric discharges and flashovers,
more probable. Avoiding this to happen clearly requires a very thorough design work; critical areas suffering from excessive
be identified followed by appropriate design modifications. Doing this by experiments
consuming and expensive. Here, numerical simulations of the electric field distribution provide a highly useful tool.
ightforward field calculation
into a statement whether a discharge or flashover
The basic mechanism behind the creation of a discharge is the ionization of the insulating gas
is the effective , which is the rate of net production
of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and
Since the ionization rate is , so is
) and the shape of this function varies
Easy Evaluation of Streamer Discharge Criteria
721 78, Västerås, Sweden
An easily implemented method is devised, where analytical criteria for the occurrence of streamer discharges in strong electric fields are evaluated. This is highly useful when designing high voltage power transmission
the insulation is
, Electric field,
In recent development of efficient power transmission systems two important trends influencing the engineering efforts are: (i) The steadily increasing voltage levels introduced to reduce resistive losses and (ii) Compacting, i.e.
to make the equipment as small as possible. From an insulation point of view, however, these two requirements are conflicting in the sense that making clearance distances between conductors at different voltage levels
increasing these voltage differences, obviously makes the
, more probable. Avoiding this to
happen clearly requires a very thorough design work; critical areas suffering from excessive
be identified followed by appropriate design modifications. Doing this by experiments
consuming and expensive. Here, numerical simulations of the electric field distribution provide a highly useful tool.
ightforward field calculation
into a statement whether a discharge or flashover
The basic mechanism behind the creation of a discharge is the ionization of the insulating gas
is the effective , which is the rate of net production
of free charges (electrons) in gas. It is equal to the ionization rate minus the recombination and
Since the ionization rate is , so is
) and the shape of this function varies
Easy Evaluation of Streamer Discharge Criteria
721 78, Västerås, Sweden, [email protected]
Easy Evaluation of Streamer Discharge Criteria
high voltage test equipment
formation of a discharge is that somewheresince lead to a macroscopically detectable discharge. For this to happen an electron avalanche must be formethe electric field causes increasing rate. independent of electrodes, will form provided the total number of electrons becomes larger than some critical number. avalanchacceleration, i.e. condition for a selfwritten
pwhere usually tsay 18.4 in what followscalled the streamer inception criterionfulfilled stationary streamer (or corona) discharge extending from the electrode, where usually
Easy Evaluation of Streamer Discharge Criteria
Figure 1
high voltage test equipment Obviously, a necessary condition for
formation of a discharge is that somewheresince lead to a macroscopically detectable discharge. For this to happen an electron avalanche must be formethe electric field causes increasing rate. independent of electrodes, will form provided the total number of electrons becomes larger than some critical number. avalanchacceleration, i.e. condition for a selfwritten
where the integral is performed along the particular field line where usually tsay 18.4 in what followscalled the streamer inception criterionfulfilled stationary streamer (or corona) discharge extending from the electrode, where usually
Easy Evaluation of Streamer Discharge Criteria
Figure 1high voltage test equipment
Obviously, a necessary condition for
formation of a discharge is that somewheresince thelead to a macroscopically detectable discharge. For this to happen an electron avalanche must be formed, i.e. each primary electronthe electric field causes increasing rate. independent of electrodes, will form provided the total number of electrons becomes larger than some critical number. avalanchacceleration, i.e. condition for a selfwritten [1,2]
where the integral is performed along the articular field line
where usually tsay 18.4 in what followscalled the streamer inception criterionfulfilled stationary streamer (or corona) discharge extending from the electrode, where usually
Easy Evaluation of Streamer Discharge Criteria
Figure 1high voltage test equipment
Obviously, a necessary condition for formation of a discharge is that somewhere
the primary electrons lead to a macroscopically detectable discharge. For this to happen an electron avalanche must be
d, i.e. each primary electronthe electric field causes increasing rate. independent of electrodes, will form provided the total number of electrons becomes larger than some critical number. If we further assume that such an avalanche will extend acceleration, i.e. condition for a self
[1,2]
=
where the integral is performed along the articular field line
eff usually taken to be in the range 15 say 18.4 in what followscalled the streamer inception criterionfulfilled it guarantees the formation of a stationary streamer (or corona) discharge extending from the electrode, where usually
Easy Evaluation of Streamer Discharge Criteria
Figure 1. Very high voltage test equipment
Obviously, a necessary condition for formation of a discharge is that somewhere. This is, however, not sufficient
primary electrons lead to a macroscopically detectable discharge. For this to happen an electron avalanche must be
d, i.e. each primary electronthe electric field causes increasing rate. independent of electrodes, will form provided the total number of electrons becomes larger than some critical
If we further assume that such an e will extend
acceleration, i.e. condition for a self
[1,2]
=
where the integral is performed along the articular field line
(E) > 0. The critical number aken to be in the range 15
say 18.4 in what followscalled the streamer inception criterion
it guarantees the formation of a stationary streamer (or corona) discharge extending from the electrode, where usually
Easy Evaluation of Streamer Discharge Criteria
Very high voltage test equipment
Obviously, a necessary condition for formation of a discharge is that
. This is, however, not sufficient primary electrons
lead to a macroscopically detectable discharge. For this to happen an electron avalanche must be
d, i.e. each primary electronthe electric field causes increasing rate. independent of electrodes, will form provided the total number of electrons becomes larger than some critical
If we further assume that such an e will extend
acceleration, i.e. along condition for a self
where the integral is performed along the articular field line
) > 0. The critical number aken to be in the range 15
say 18.4 in what followscalled the streamer inception criterion
it guarantees the formation of a stationary streamer (or corona) discharge extending from the electrode, where usually
Very long discharges created with a high voltage test equipment
Obviously, a necessary condition for formation of a discharge is that
. This is, however, not sufficient primary electrons
lead to a macroscopically detectable discharge. For this to happen an electron avalanche must be
d, i.e. each primary electronthe electric field causes increasing rate. A selfindependent of charge injection from the electrodes, will form provided the total number of electrons becomes larger than some critical
If we further assume that such an e will extend
along condition for a self-sustained avalanche can be
(
where the integral is performed along the articular field line under consideration
) > 0. The critical number aken to be in the range 15
say 18.4 in what followscalled the streamer inception criterion
it guarantees the formation of a stationary streamer (or corona) discharge extending from the electrode, where usually
long discharges created with a high voltage test equipment
Obviously, a necessary condition for formation of a discharge is that
. This is, however, not sufficient primary electrons
lead to a macroscopically detectable discharge. For this to happen an electron avalanche must be
d, i.e. each primary electronthe electric field causes
A selfcharge injection from the
electrodes, will form provided the total number of electrons becomes larger than some critical
If we further assume that such an e will extend in the direction of electron
along an electric field linesustained avalanche can be
( )
where the integral is performed along the under consideration
) > 0. The critical number aken to be in the range 15
say 18.4 in what followscalled the streamer inception criterion
it guarantees the formation of a stationary streamer (or corona) discharge extending from the electrode, where usually
long discharges created with a high voltage test equipment.
Obviously, a necessary condition for formation of a discharge is that
. This is, however, not sufficient primary electrons
lead to a macroscopically detectable discharge. For this to happen an electron avalanche must be
d, i.e. each primary electronthe electric field causes further
A self-sustcharge injection from the
electrodes, will form provided the total number of electrons becomes larger than some critical
If we further assume that such an in the direction of electron
an electric field linesustained avalanche can be
( ) >
where the integral is performed along the under consideration
) > 0. The critical number aken to be in the range 15
say 18.4 in what follows The above criterion is called the streamer inception criterion
it guarantees the formation of a stationary streamer (or corona) discharge extending from the electrode, where usually
long discharges created with a
Obviously, a necessary condition for formation of a discharge is that
. This is, however, not sufficient primary electrons themselves
lead to a macroscopically detectable discharge. For this to happen an electron avalanche must be
d, i.e. each primary electronfurther
sustcharge injection from the
electrodes, will form provided the total number of electrons becomes larger than some critical
If we further assume that such an in the direction of electron
an electric field linesustained avalanche can be
>
where the integral is performed along the under consideration
) > 0. The critical number aken to be in the range 15
The above criterion is called the streamer inception criterion
it guarantees the formation of a stationary streamer (or corona) discharge extending from the electrode, where usually
long discharges created with a
Obviously, a necessary condition for formation of a discharge is that
. This is, however, not sufficient themselves
lead to a macroscopically detectable discharge. For this to happen an electron avalanche must be
d, i.e. each primary electron further ionization at an
sustained discharge, charge injection from the
electrodes, will form provided the total number of electrons becomes larger than some critical
If we further assume that such an in the direction of electron
an electric field linesustained avalanche can be
where the integral is performed along the under consideration
) > 0. The critical number aken to be in the range 15
The above criterion is called the streamer inception criterion
it guarantees the formation of a stationary streamer (or corona) discharge extending from the electrode, where usually
long discharges created with a
Obviously, a necessary condition for formation of a discharge is that
. This is, however, not sufficient themselves
lead to a macroscopically detectable discharge. For this to happen an electron avalanche must be
acceleionization at an
ained discharge, charge injection from the
electrodes, will form provided the total number of electrons becomes larger than some critical
If we further assume that such an in the direction of electron
an electric field linesustained avalanche can be
where the integral is performed along the under consideration
) > 0. The critical number aken to be in the range 15 -
The above criterion is called the streamer inception criterion
it guarantees the formation of a stationary streamer (or corona) discharge extending from the electrode, where usually
long discharges created with a
Obviously, a necessary condition for formation of a discharge is that eff
. This is, however, not sufficient themselves will not
lead to a macroscopically detectable discharge. For this to happen an electron avalanche must be
accelerated in ionization at an
ained discharge, charge injection from the
electrodes, will form provided the total number of electrons becomes larger than some critical
If we further assume that such an in the direction of electron
an electric field linesustained avalanche can be
where the integral is performed along the under consideration and only
) > 0. The critical number - 20, let us
The above criterion is called the streamer inception criterion. If it is
it guarantees the formation of a stationary streamer (or corona) discharge extending from the electrode, where usually
long discharges created with a
Obviously, a necessary condition for eff > 0
. This is, however, not sufficient will not
lead to a macroscopically detectable discharge. For this to happen an electron avalanche must be
rated in ionization at an
ained discharge, charge injection from the
electrodes, will form provided the total number of electrons becomes larger than some critical
If we further assume that such an in the direction of electron
an electric field line, the sustained avalanche can be
where the integral is performed along the and only
) > 0. The critical number Ccrit20, let us
The above criterion is . If it is
it guarantees the formation of a stationary streamer (or corona) discharge extending from the electrode, where usually
long discharges created with a
Obviously, a necessary condition for the > 0
. This is, however, not sufficient will not
lead to a macroscopically detectable discharge. For this to happen an electron avalanche must be
rated in ionization at an
ained discharge, charge injection from the
electrodes, will form provided the total number of electrons becomes larger than some critical
If we further assume that such an in the direction of electron
, the sustained avalanche can be
(1)
where the integral is performed along the and only
crit is 20, let us
The above criterion is . If it is
it guarantees the formation of a stationary streamer (or corona) discharge extending from the electrode, where usually
long discharges created with a
the > 0
. This is, however, not sufficient will not
lead to a macroscopically detectable discharge. For this to happen an electron avalanche must be
rated in ionization at an
ained discharge, charge injection from the
electrodes, will form provided the total number of electrons becomes larger than some critical
If we further assume that such an in the direction of electron
, the sustained avalanche can be
(1)
where the integral is performed along the and only
is 20, let us
The above criterion is . If it is
it guarantees the formation of a stationary streamer (or corona) discharge extending from the electrode, where usually
the high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
still a chance for a comphappen ifstreamer head is so high that the ionization forward. This process, called streamer propagation, field
Here electrodes, line, Epositive electrode and discharge starting from the negative electrode.
where the conductivestreamer head enmore or less independently of the external field.
electrostatic field to evaluate the aboveprcommercial field solver is to analyze a large number of field lines at the same time and to postresult in an instructive way. inpossible to analyze a limited number of field lines
Multiphysics there has been no easily implemented method to perform the integrals along field lines, although done by formulating the problem in terms of an additional partial diffesolved [3introducedMultiphysicsbe computed and analyzed in a mostraightforward and implementation is simple and a large number of field lines can be evaluated simultaneously, both
eff(Eeff (E
If the high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
eff (still a chance for a comphappen ifstreamer head is so high that the ionization forward. This process, called streamer propagation, field
Here electrodes, line, E0 0.5 kV/mm for a discharge starting from the positive electrode and discharge starting from the negative electrode.
Here, we don´t consider leader propagation, where the conductivestreamer head enmore or less independently of the external field.
Although the computation of the background electrostatic field to evaluate the abovepreviously commercial field solver is to analyze a large number of field lines at the same time and to postresult in an instructive way. in-house developed possible to analyze a limited number of field lines
In previous versions of COMSOL Multiphysics there has been no easily implemented method to perform the integrals along field lines, although done by formulating the problem in terms of an additional partial diffesolved [3introducedMultiphysicsbe computed and analyzed in a mostraightforward and implementation is simple and a large number of field lines can be evaluated simultaneously, both
E) has its maximum, out to the surface where E) = 0.
If effthe high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
(E) < 0 along parts of the field line there is still a chance for a comphappen ifstreamer head is so high that the ionization forward. This process, called streamer propagation, field
Here U electrodes, line, U0
0.5 kV/mm for a discharge starting from the positive electrode and discharge starting from the negative electrode.
Here, we don´t consider leader propagation, where the conductivestreamer head enmore or less independently of the external field.
Although the computation of the background electrostatic field to evaluate the above
eviously commercial field solver is to analyze a large number of field lines at the same time and to postresult in an instructive way.
house developed possible to analyze a limited number of field
simultaneouslyIn previous versions of COMSOL
Multiphysics there has been no easily implemented method to perform the integrals along field lines, although done by formulating the problem in terms of an additional partial diffesolved [3introducedMultiphysicsbe computed and analyzed in a mostraightforward and implementation is simple and a large number of field lines can be evaluated simultaneously, both
) has its maximum, out to the surface where ) = 0.
eff (Ethe high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
) < 0 along parts of the field line there is still a chance for a comphappen if the electric field just in front of the streamer head is so high that the ionization effectively moves the streamer head forward. This process, called streamer propagation,
along the field line satisfies
U is the voltage difference between the electrodes,
1 0.5 kV/mm for a discharge starting from the
positive electrode and discharge starting from the negative electrode.
Here, we don´t consider leader propagation, where the conductive streamer head enmore or less independently of the external field.
Although the computation of the background electrostatic field to evaluate the above
eviously commercial field solver is to analyze a large number of field lines at the same time and to postresult in an instructive way.
house developed possible to analyze a limited number of field
simultaneouslyIn previous versions of COMSOL
Multiphysics there has been no easily implemented method to perform the integrals along field lines, although done by formulating the problem in terms of an additional partial diffesolved [3]. introduced Multiphysicsbe computed and analyzed in a mostraightforward and implementation is simple and a large number of field lines can be evaluated simultaneously, both
) has its maximum, out to the surface where
E) >the high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
) < 0 along parts of the field line there is still a chance for a comp
the electric field just in front of the streamer head is so high that the
effectively moves the streamer head forward. This process, called streamer propagation, can take place provided the ave
along the field line satisfies
=
is the voltage difference between the electrodes, =
10-30 kV is an empirical constant, and 0.5 kV/mm for a discharge starting from the
positive electrode and discharge starting from the negative electrode.
Here, we don´t consider leader propagation, where the hot
that the field enhancstreamer head enmore or less independently of the external field.
Although the computation of the background electrostatic field to evaluate the above
eviously not commercial field solver is to analyze a large number of field lines at the same time and to postresult in an instructive way.
house developed possible to analyze a limited number of field
simultaneouslyIn previous versions of COMSOL
Multiphysics there has been no easily implemented method to perform the integrals along field lines, although done by formulating the problem in terms of an additional partial diffe
Using the Particle Tracing Module in version 4.3 of COMSOL
Multiphysics, such field line integrals can now be computed and analyzed in a mostraightforward and implementation is simple and a large number of field lines can be evaluated simultaneously, both
) has its maximum, out to the surface where
) > 0 along the entire field line, from the high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
) < 0 along parts of the field line there is still a chance for a comp
the electric field just in front of the streamer head is so high that the
effectively moves the streamer head forward. This process, called streamer
can take place provided the avealong the field line satisfies
is the voltage difference between the =30 kV is an empirical constant, and
0.5 kV/mm for a discharge starting from the positive electrode and discharge starting from the negative electrode.
Here, we don´t consider leader propagation, hot plasma channel becomes so that the field enhanc
streamer head enables the streamer to propagatemore or less independently of the external field.
Although the computation of the background electrostatic field Eto evaluate the above
not been commercial field solver is to analyze a large number of field lines at the same time and to postresult in an instructive way.
house developed possible to analyze a limited number of field
simultaneouslyIn previous versions of COMSOL
Multiphysics there has been no easily implemented method to perform the integrals along field lines, although done by formulating the problem in terms of an additional partial diffe
Using the Particle Tracing Modulein version 4.3 of COMSOL
such field line integrals can now be computed and analyzed in a mostraightforward and implementation is simple and a large number of field lines can be evaluated simultaneously, both
) has its maximum, out to the surface where
0 along the entire field line, from the high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
) < 0 along parts of the field line there is still a chance for a comp
the electric field just in front of the streamer head is so high that the
effectively moves the streamer head forward. This process, called streamer
can take place provided the avealong the field line satisfies
>
is the voltage difference between the
30 kV is an empirical constant, and 0.5 kV/mm for a discharge starting from the
positive electrode and discharge starting from the negative electrode.
Here, we don´t consider leader propagation, plasma channel becomes so
that the field enhancables the streamer to propagate
more or less independently of the external field.Although the computation of the background
E is straightforward, tto evaluate the above
been commercial field solver is to analyze a large number of field lines at the same time and to postresult in an instructive way.
house developed possible to analyze a limited number of field
simultaneously. In previous versions of COMSOL
Multiphysics there has been no easily implemented method to perform the integrals along field lines, although done by formulating the problem in terms of an additional partial diffe
Using the Particle Tracing Modulein version 4.3 of COMSOL
such field line integrals can now be computed and analyzed in a mostraightforward and implementation is simple and a large number of field lines can be evaluated simultaneously, both
) has its maximum, out to the surface where
0 along the entire field line, from the high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
) < 0 along parts of the field line there is still a chance for a complete flashover.
the electric field just in front of the streamer head is so high that the
effectively moves the streamer head forward. This process, called streamer
can take place provided the avealong the field line satisfies
>
is the voltage difference between the is the length of the field
30 kV is an empirical constant, and 0.5 kV/mm for a discharge starting from the
positive electrode and Edischarge starting from the negative electrode.
Here, we don´t consider leader propagation, plasma channel becomes so
that the field enhancables the streamer to propagate
more or less independently of the external field.Although the computation of the background
is straightforward, tto evaluate the above-mentioned criteria has
been commercial field solver software. is to analyze a large number of field lines at the same time and to post process and visualize the result in an instructive way.
house developed codespossible to analyze a limited number of field
In previous versions of COMSOL
Multiphysics there has been no easily implemented method to perform the integrals along field lines, although done by formulating the problem in terms of an additional partial differential equation to be
Using the Particle Tracing Modulein version 4.3 of COMSOL
such field line integrals can now be computed and analyzed in a mostraightforward and implementation is simple and a large number of field lines can be evaluated simultaneously, both
) has its maximum, out to the surface where
0 along the entire field line, from the high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
) < 0 along parts of the field line there is lete flashover.
the electric field just in front of the streamer head is so high that the
effectively moves the streamer head forward. This process, called streamer
can take place provided the avealong the field line satisfies
is the voltage difference between the is the length of the field
30 kV is an empirical constant, and 0.5 kV/mm for a discharge starting from the
E0 1.2 kV/mm for a discharge starting from the negative electrode.
Here, we don´t consider leader propagation, plasma channel becomes so
that the field enhancables the streamer to propagate
more or less independently of the external field.Although the computation of the background
is straightforward, tmentioned criteria has
been available in standard software.
is to analyze a large number of field lines at the process and visualize the
result in an instructive way. codes
possible to analyze a limited number of field
In previous versions of COMSOL Multiphysics there has been no easily implemented method to perform the integrals along field lines, although it can in principle be done by formulating the problem in terms of an
rential equation to be Using the Particle Tracing Modulein version 4.3 of COMSOL
such field line integrals can now be computed and analyzed in a mostraightforward and efficientimplementation is simple and a large number of field lines can be evaluated simultaneously, both
) has its maximum, out to the surface where
0 along the entire field line, from the high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
) < 0 along parts of the field line there is lete flashover.
the electric field just in front of the streamer head is so high that the
effectively moves the streamer head forward. This process, called streamer
can take place provided the avealong the field line satisfies
+
is the voltage difference between the is the length of the field
30 kV is an empirical constant, and 0.5 kV/mm for a discharge starting from the
1.2 kV/mm for a discharge starting from the negative electrode.
Here, we don´t consider leader propagation, plasma channel becomes so
that the field enhancables the streamer to propagate
more or less independently of the external field.Although the computation of the background
is straightforward, tmentioned criteria has available in standard software.
is to analyze a large number of field lines at the process and visualize the
result in an instructive way. Even in specialized it has only been
possible to analyze a limited number of field
In previous versions of COMSOL Multiphysics there has been no easily implemented method to perform the integrals
it can in principle be done by formulating the problem in terms of an
rential equation to be Using the Particle Tracing Modulein version 4.3 of COMSOL
such field line integrals can now be computed and analyzed in a mo
efficientimplementation is simple and a large number of field lines can be evaluated simultaneously, both
) has its maximum, out to the surface where
0 along the entire field line, from the high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
) < 0 along parts of the field line there is lete flashover.
the electric field just in front of the streamer head is so high that the associated
effectively moves the streamer head forward. This process, called streamer
can take place provided the avealong the field line satisfies
.
is the voltage difference between the is the length of the field
30 kV is an empirical constant, and 0.5 kV/mm for a discharge starting from the
1.2 kV/mm for a discharge starting from the negative electrode.
Here, we don´t consider leader propagation, plasma channel becomes so
that the field enhancement at the ables the streamer to propagate
more or less independently of the external field.Although the computation of the background
is straightforward, tmentioned criteria has available in standard software. The challenge
is to analyze a large number of field lines at the process and visualize the
Even in specialized it has only been
possible to analyze a limited number of field
In previous versions of COMSOL Multiphysics there has been no easily implemented method to perform the integrals
it can in principle be done by formulating the problem in terms of an
rential equation to be Using the Particle Tracing Modulein version 4.3 of COMSOL
such field line integrals can now be computed and analyzed in a mo
efficient implementation is simple and a large number of field lines can be evaluated simultaneously, both
) has its maximum, out to the surface where
0 along the entire field line, from the high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
) < 0 along parts of the field line there is lete flashover.
the electric field just in front of the associated
effectively moves the streamer head forward. This process, called streamer
can take place provided the avealong the field line satisfies [2]
is the voltage difference between the is the length of the field
30 kV is an empirical constant, and 0.5 kV/mm for a discharge starting from the
1.2 kV/mm for a discharge starting from the negative electrode.
Here, we don´t consider leader propagation, plasma channel becomes so
ement at the ables the streamer to propagate
more or less independently of the external field.Although the computation of the background
is straightforward, tmentioned criteria has available in standard
The challenge is to analyze a large number of field lines at the
process and visualize the Even in specialized it has only been
possible to analyze a limited number of field
In previous versions of COMSOL Multiphysics there has been no easily implemented method to perform the integrals
it can in principle be done by formulating the problem in terms of an
rential equation to be Using the Particle Tracing Modulein version 4.3 of COMSOL
such field line integrals can now be computed and analyzed in a mo
way. The implementation is simple and a large number of field lines can be evaluated simultaneously, both
) has its maximum, out to the surface where
0 along the entire field line, from the high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
) < 0 along parts of the field line there is lete flashover. This may
the electric field just in front of the associated
effectively moves the streamer head forward. This process, called streamer
can take place provided the ave[2]
is the voltage difference between the is the length of the field
30 kV is an empirical constant, and 0.5 kV/mm for a discharge starting from the
1.2 kV/mm for a discharge starting from the negative electrode.
Here, we don´t consider leader propagation, plasma channel becomes so
ement at the ables the streamer to propagate
more or less independently of the external field.Although the computation of the background
is straightforward, the ability mentioned criteria has available in standard
The challenge is to analyze a large number of field lines at the
process and visualize the Even in specialized it has only been
possible to analyze a limited number of field
In previous versions of COMSOL Multiphysics there has been no easily implemented method to perform the integrals
it can in principle be done by formulating the problem in terms of an
rential equation to be Using the Particle Tracing Modulein version 4.3 of COMSOL
such field line integrals can now be computed and analyzed in a mo
way. The implementation is simple and a large number of field lines can be evaluated simultaneously, both
) has its maximum, out to the surface where
0 along the entire field line, from the high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
) < 0 along parts of the field line there is This may
the electric field just in front of the associated field
effectively moves the streamer head forward. This process, called streamer
can take place provided the average
is the voltage difference between the is the length of the field
30 kV is an empirical constant, and 0.5 kV/mm for a discharge starting from the
1.2 kV/mm for a discharge starting from the negative electrode.
Here, we don´t consider leader propagation, plasma channel becomes so
ement at the ables the streamer to propagate
more or less independently of the external field.Although the computation of the background
he ability mentioned criteria has available in standard
The challenge is to analyze a large number of field lines at the
process and visualize the Even in specialized it has only been
possible to analyze a limited number of field
In previous versions of COMSOL Multiphysics there has been no easily implemented method to perform the integrals
it can in principle be done by formulating the problem in terms of an
rential equation to be Using the Particle Tracing Modulein version 4.3 of COMSOL
such field line integrals can now be computed and analyzed in a mo
way. The implementation is simple and a large number of field lines can be evaluated simultaneously, both
) has its maximum, out to the surface where
0 along the entire field line, from the high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
) < 0 along parts of the field line there is This may
the electric field just in front of the field
effectively moves the streamer head forward. This process, called streamer
rage
(2)
is the voltage difference between the is the length of the field
30 kV is an empirical constant, and 0.5 kV/mm for a discharge starting from the
1.2 kV/mm for a discharge starting from the negative electrode.
Here, we don´t consider leader propagation, plasma channel becomes so
ement at the ables the streamer to propagate,
more or less independently of the external field. Although the computation of the background
he ability mentioned criteria has available in standard
The challenge is to analyze a large number of field lines at the
process and visualize the Even in specialized it has only been
possible to analyze a limited number of field
In previous versions of COMSOL Multiphysics there has been no easily implemented method to perform the integrals
it can in principle be done by formulating the problem in terms of an
rential equation to be Using the Particle Tracing Modulein version 4.3 of COMSOL
such field line integrals can now be computed and analyzed in a more
way. The implementation is simple and a large number of field lines can be evaluated simultaneously, both
) has its maximum, out to the surface where
0 along the entire field line, from the high voltage to the grounded electrode, the fulfillment of (1) will lead to an immediate breakdown across the gap. If, on the other hand,
) < 0 along parts of the field line there is This may
the electric field just in front of the field
effectively moves the streamer head forward. This process, called streamer
rage
(2)
is the voltage difference between the is the length of the field
30 kV is an empirical constant, and 0.5 kV/mm for a discharge starting from the
1.2 kV/mm for a
Here, we don´t consider leader propagation, plasma channel becomes so
ement at the ,
Although the computation of the background he ability
mentioned criteria has available in standard
The challenge is to analyze a large number of field lines at the
process and visualize the Even in specialized it has only been
possible to analyze a limited number of field
In previous versions of COMSOL Multiphysics there has been no easily implemented method to perform the integrals
it can in principle be done by formulating the problem in terms of an
rential equation to be Using the Particle Tracing Module in version 4.3 of COMSOL
such field line integrals can now re
way. The implementation is simple and a large number of field lines can be evaluated simultaneously, both
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization process of insulation desigequipment.
way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some applications involving 2D and 3D geomprovided
2
some words should be said about the effective ionization function depending on the insulating gas. For air it can be approximated by a quadratic formula
bar), and 0.3 1/(mm bar). in bar.therefore is the net production of charge carriers to occur.
3 3
viz. Tracingafter the other, in two different Studies. First, the Electrostaticsproblem in Study 1, providing the electrostatic background field. Then, the time dependent Charged Particle Tracing problem2, evaluating the streamer criteria integrals for each field line.
3.2 Electrostatic background field
procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an openingsurrounded by a flange that complicates the field pattern and the solution. After running Study 1,
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization process of insulation desigequipment.
In the present contribution we describe the way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some applications involving 2D and 3D geomprovided
2. Effective ionization function
Before proceeding to the solution procedure some words should be said about the effective ionization function depending on the insulating gas. For air it can be approximated by a quadratic formula
Here,
bar), and 0.3 1/(mm bar). in bar.therefore is the net production of charge carriers to occur.
3. Solution procedure 3.1 General
The model includes two physical interfaces, viz. Tracingafter the other, in two different Studies. First, the Electrostaticsproblem in Study 1, providing the electrostatic background field. Then, the time dependent Charged Particle Tracing problem2, evaluating the streamer criteria integrals for each field line.
3.2 Electrostatic background field
For the purpose of demonstrating the procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an openingsurrounded by a flange that complicates the field pattern and the solution. After running Study 1,
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization process of insulation desigequipment.
In the present contribution we describe the way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some applications involving 2D and 3D geomprovided
Effective ionization function
Before proceeding to the solution procedure some words should be said about the effective ionization function depending on the insulating gas. For air it can be approximated by a quadratic formula
Here,
bar), and 0.3 1/(mm bar). in bar. therefore is the net production of charge carriers to occur.
Solution procedure
.1 General
The model includes two physical interfaces, viz. ElectrostaticsTracingafter the other, in two different Studies. First, the Electrostaticsproblem in Study 1, providing the electrostatic background field. Then, the time dependent Charged Particle Tracing problem2, evaluating the streamer criteria integrals for each field line.
3.2 Electrostatic background field
For the purpose of demonstrating the procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an openingsurrounded by a flange that complicates the field pattern and the solution. After running Study 1,
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization process of insulation desigequipment.
In the present contribution we describe the way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some applications involving 2D and 3D geomprovided.
Effective ionization function
Before proceeding to the solution procedure some words should be said about the effective ionization function depending on the insulating gas. For air it can be approximated by a quadratic formula
Here, k bar), and 0.3 1/(mm bar).
eff therefore is the net production of charge carriers to occur.
Solution procedure
.1 General
The model includes two physical interfaces, Electrostatics
Tracing, see Fig. 2after the other, in two different Studies. First, the Electrostaticsproblem in Study 1, providing the electrostatic background field. Then, the time dependent Charged Particle Tracing problem2, evaluating the streamer criteria integrals for each field line.
3.2 Electrostatic background field
For the purpose of demonstrating the procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an opening in a grounded wall. The hole is surrounded by a flange that complicates the field pattern and the solution. After running Study 1,
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization process of insulation desigequipment.
In the present contribution we describe the way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some applications involving 2D and 3D geom
Effective ionization function
Before proceeding to the solution procedure some words should be said about the effective ionization function depending on the insulating gas. For air it can be approximated by a quadratic formula
) =
k = 1.6 mm bar /kVbar), and 0.3 1/(mm bar).
eff (E) > 0 for therefore is the net production of charge carriers to occur.
Solution procedure
.1 General
The model includes two physical interfaces, Electrostatics
, see Fig. 2after the other, in two different Studies. First, the Electrostatics problem in Study 1, providing the electrostatic background field. Then, the time dependent Charged Particle Tracing problem2, evaluating the streamer criteria integrals for each field line.
3.2 Electrostatic background field
For the purpose of demonstrating the procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an
in a grounded wall. The hole is surrounded by a flange that complicates the field pattern and the solution. After running Study 1,
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization process of insulation desig
In the present contribution we describe the way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some applications involving 2D and 3D geom
Effective ionization function
Before proceeding to the solution procedure some words should be said about the effective ionization function depending on the insulating gas. For air it can be approximated by a quadratic formula
=
= 1.6 mm bar /kVbar), and 0.3 1/(mm bar).
) > 0 for therefore is the criticanet production of charge carriers to occur.
Solution procedure
The model includes two physical interfaces, Electrostatics
, see Fig. 2after the other, in two different Studies. First, the
problem is solved as a stationary problem in Study 1, providing the electrostatic background field. Then, the time dependent Charged Particle Tracing problem2, evaluating the streamer criteria integrals for each field line.
3.2 Electrostatic background field
For the purpose of demonstrating the procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an
in a grounded wall. The hole is surrounded by a flange that complicates the field pattern and the solution. After running Study 1,
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization process of insulation desig
In the present contribution we describe the way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some applications involving 2D and 3D geom
Effective ionization function
Before proceeding to the solution procedure some words should be said about the effective ionization function effdepending on the insulating gas. For air it can be approximated by a quadratic formula
= 1.6 mm bar /kVbar), and 0.3 1/(mm bar).
) > 0 for critica
net production of charge carriers to occur.
Solution procedure
The model includes two physical interfaces, Electrostatics
, see Fig. 2. These are run separately, one after the other, in two different Studies. First, the
problem is solved as a stationary problem in Study 1, providing the electrostatic background field. Then, the time dependent Charged Particle Tracing problem2, evaluating the streamer criteria integrals for
3.2 Electrostatic background field
For the purpose of demonstrating the procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an
in a grounded wall. The hole is surrounded by a flange that complicates the field pattern and the solution. After running Study 1,
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization process of insulation desig
In the present contribution we describe the way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some applications involving 2D and 3D geom
Effective ionization function
Before proceeding to the solution procedure some words should be said about the effective
eff (Edepending on the insulating gas. For air it can be approximated by a quadratic formula
= 1.6 mm bar /kVbar), and 0.3 1/(mm bar).
) > 0 for critical field strength needed
net production of charge carriers to occur.
Solution procedure
The model includes two physical interfaces, and These are run separately, one
after the other, in two different Studies. First, the problem is solved as a stationary
problem in Study 1, providing the electrostatic background field. Then, the time dependent Charged Particle Tracing problem2, evaluating the streamer criteria integrals for
3.2 Electrostatic background field
For the purpose of demonstrating the procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an
in a grounded wall. The hole is surrounded by a flange that complicates the field pattern and the solution. After running Study 1,
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization process of insulation desig
In the present contribution we describe the way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some applications involving 2D and 3D geom
Effective ionization function
Before proceeding to the solution procedure some words should be said about the effective
E). It behaves differently depending on the insulating gas. For air it can be approximated by a quadratic formula
= 1.6 mm bar /kVbar), and 0.3 1/(mm bar). p
) > 0 for E > 2.6 kV/mm, which l field strength needed
net production of charge carriers to occur.
Solution procedure
The model includes two physical interfaces, and
These are run separately, one after the other, in two different Studies. First, the
problem is solved as a stationary problem in Study 1, providing the electrostatic background field. Then, the time dependent Charged Particle Tracing problem2, evaluating the streamer criteria integrals for
3.2 Electrostatic background field
For the purpose of demonstrating the procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an
in a grounded wall. The hole is surrounded by a flange that complicates the field pattern and the solution. After running Study 1,
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization process of insulation designs in high voltage
In the present contribution we describe the way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some applications involving 2D and 3D geom
Effective ionization function
Before proceeding to the solution procedure some words should be said about the effective
It behaves differently depending on the insulating gas. For air it can be approximated by a quadratic formula
= 1.6 mm bar /kV2, is the pressure given > 2.6 kV/mm, which
l field strength needednet production of charge carriers to occur.
The model includes two physical interfaces, and Charged Particle
These are run separately, one after the other, in two different Studies. First, the
problem is solved as a stationary problem in Study 1, providing the electrostatic background field. Then, the time dependent Charged Particle Tracing problem2, evaluating the streamer criteria integrals for
3.2 Electrostatic background field
For the purpose of demonstrating the procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an
in a grounded wall. The hole is surrounded by a flange that complicates the field pattern and the solution. After running Study 1,
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization
ns in high voltage
In the present contribution we describe the way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some applications involving 2D and 3D geom
Effective ionization function
Before proceeding to the solution procedure some words should be said about the effective
It behaves differently depending on the insulating gas. For air it can be approximated by a quadratic formula
.
, = 2.2 kV/(mm is the pressure given
> 2.6 kV/mm, which l field strength needed
net production of charge carriers to occur.
The model includes two physical interfaces, Charged Particle
These are run separately, one after the other, in two different Studies. First, the
problem is solved as a stationary problem in Study 1, providing the electrostatic background field. Then, the time dependent Charged Particle Tracing problem is run in Study 2, evaluating the streamer criteria integrals for
3.2 Electrostatic background field
For the purpose of demonstrating the procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an
in a grounded wall. The hole is surrounded by a flange that complicates the field pattern and the solution. After running Study 1,
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization
ns in high voltage
In the present contribution we describe the way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some applications involving 2D and 3D geom
Effective ionization function
Before proceeding to the solution procedure some words should be said about the effective
It behaves differently depending on the insulating gas. For air it can be approximated by a quadratic formula [4
.
= 2.2 kV/(mm is the pressure given
> 2.6 kV/mm, which l field strength needed
net production of charge carriers to occur.
The model includes two physical interfaces, Charged Particle
These are run separately, one after the other, in two different Studies. First, the
problem is solved as a stationary problem in Study 1, providing the electrostatic background field. Then, the time dependent
is run in Study 2, evaluating the streamer criteria integrals for
3.2 Electrostatic background field
For the purpose of demonstrating the procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an
in a grounded wall. The hole is surrounded by a flange that complicates the field pattern and the solution. After running Study 1,
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization
ns in high voltage
In the present contribution we describe the way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some applications involving 2D and 3D geometries are
Before proceeding to the solution procedure some words should be said about the effective
It behaves differently depending on the insulating gas. For air it can be
[4]:
= 2.2 kV/(mm is the pressure given
> 2.6 kV/mm, which l field strength needed
net production of charge carriers to occur.
The model includes two physical interfaces, Charged Particle
These are run separately, one after the other, in two different Studies. First, the
problem is solved as a stationary problem in Study 1, providing the electrostatic background field. Then, the time dependent
is run in Study 2, evaluating the streamer criteria integrals for
For the purpose of demonstrating the procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an
in a grounded wall. The hole is surrounded by a flange that complicates the field pattern and the solution. After running Study 1,
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization
ns in high voltage
In the present contribution we describe the way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some
etries are
Before proceeding to the solution procedure some words should be said about the effective
It behaves differently depending on the insulating gas. For air it can be
= 2.2 kV/(mm is the pressure given
> 2.6 kV/mm, which l field strength needed for a
net production of charge carriers to occur.
The model includes two physical interfaces, Charged Particle
These are run separately, one after the other, in two different Studies. First, the
problem is solved as a stationary problem in Study 1, providing the electrostatic background field. Then, the time dependent
is run in Study 2, evaluating the streamer criteria integrals for
For the purpose of demonstrating the procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an
in a grounded wall. The hole is surrounded by a flange that complicates the field pattern and the solution. After running Study 1,
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization
ns in high voltage
In the present contribution we describe the way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some
etries are
Before proceeding to the solution procedure some words should be said about the effective
It behaves differently depending on the insulating gas. For air it can be
(3)
= 2.2 kV/(mm is the pressure given
> 2.6 kV/mm, which for a
The model includes two physical interfaces, Charged Particle
These are run separately, one after the other, in two different Studies. First, the
problem is solved as a stationary problem in Study 1, providing the electrostatic background field. Then, the time dependent
is run in Study 2, evaluating the streamer criteria integrals for
For the purpose of demonstrating the procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an
in a grounded wall. The hole is surrounded by a flange that complicates the field pattern and the solution. After running Study 1,
in 2D and 3D. Hopefully, this will result in a much faster and more reliable optimization
ns in high voltage
In the present contribution we describe the way to apply the massless particle tracing technique in order to compute the integrals, as well as an example of how the results can be presented in an intuitive manner. Some
etries are
Before proceeding to the solution procedure some words should be said about the effective
It behaves differently depending on the insulating gas. For air it can be
(3)
= 2.2 kV/(mm is the pressure given
> 2.6 kV/mm, which for a
The model includes two physical interfaces, Charged Particle
These are run separately, one after the other, in two different Studies. First, the
problem is solved as a stationary problem in Study 1, providing the electrostatic background field. Then, the time dependent
is run in Study 2, evaluating the streamer criteria integrals for
For the purpose of demonstrating the procedure we use an axisymmetric model of a high voltage (105 kV) conductor penetrating an
in a grounded wall. The hole is surrounded by a flange that complicates the field
displayed in the Model Builder
theNote the regions where value 2.6 kV/mm required for net charge production.
3.3 Particle Tracing
calculated we can turn to the evaluation of the streamer integrals. Charged Particle Tracingthis node we define the 4.
originally intended for calculating trajectories of moving charged partimagnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node (Charged Particle Tracingunder the Massless
selecting those surfaces from which the field lines are starting. This is done under the node. Also, the number of field lines ("particles") is entered. Preferably one selects all sureither high or zero potential in order to make sure that all field lines are included in the analysis.
Figure displayed in the Model Builder
the electric fielNote the regions where value 2.6 kV/mm required for net charge production.
3.3 Particle Tracing
Once the background electric field is calculated we can turn to the evaluation of the treamer integrals.
Charged Particle Tracingthis node we define the
. The
originally intended for calculating trajectories of moving charged partimagnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node Charged Particle Tracing
under the Massless
The particle tracing procedure starts by selecting those surfaces from which the field lines are starting. This is done under the node. Also, the number of field lines ("particles") is entered. Preferably one selects all sureither high or zero potential in order to make sure that all field lines are included in the analysis.
Figure displayed in the Model Builder
electric fielNote the regions where value 2.6 kV/mm required for net charge production.
3.3 Particle Tracing
Once the background electric field is calculated we can turn to the evaluation of the treamer integrals.
Charged Particle Tracingthis node we define the
The originally intended for calculating trajectories of moving charged partimagnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node Charged Particle Tracing
under the Massless
The particle tracing procedure starts by selecting those surfaces from which the field lines are starting. This is done under the node. Also, the number of field lines ("particles") is entered. Preferably one selects all sureither high or zero potential in order to make sure that all field lines are included in the analysis.
Figure 2displayed in the Model Builder
electric fielNote the regions where value 2.6 kV/mm required for net charge production.
3.3 Particle Tracing
Once the background electric field is calculated we can turn to the evaluation of the treamer integrals.
Charged Particle Tracingthis node we define the
The Charged Particle Tracingoriginally intended for calculating trajectories of moving charged partimagnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node Charged Particle Tracing
under the Massless formulation.
The particle tracing procedure starts by selecting those surfaces from which the field lines are starting. This is done under the node. Also, the number of field lines ("particles") is entered. Preferably one selects all sureither high or zero potential in order to make sure that all field lines are included in the analysis.
2. The general structure of the model displayed in the Model Builder
electric fielNote the regions where value 2.6 kV/mm required for net charge
3.3 Particle Tracing
Once the background electric field is calculated we can turn to the evaluation of the treamer integrals.
Charged Particle Tracingthis node we define the
Charged Particle Tracingoriginally intended for calculating trajectories of moving charged partimagnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node Charged Particle Tracing
under the Particle Propertiesformulation.
The particle tracing procedure starts by selecting those surfaces from which the field lines are starting. This is done under the node. Also, the number of field lines ("particles") is entered. Preferably one selects all sureither high or zero potential in order to make sure that all field lines are included in the
The general structure of the model displayed in the Model Builder
electric field is found as is shown in Fig. 3Note the regions where value 2.6 kV/mm required for net charge
3.3 Particle Tracing
Once the background electric field is calculated we can turn to the evaluation of the treamer integrals.
Charged Particle Tracingthis node we define the
Charged Particle Tracingoriginally intended for calculating trajectories of moving charged partimagnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node Charged Particle Tracing
Particle Propertiesformulation.
The particle tracing procedure starts by selecting those surfaces from which the field lines are starting. This is done under the node. Also, the number of field lines ("particles") is entered. Preferably one selects all sureither high or zero potential in order to make sure that all field lines are included in the
The general structure of the model displayed in the Model Builder
d is found as is shown in Fig. 3Note the regions where value 2.6 kV/mm required for net charge
3.3 Particle Tracing
Once the background electric field is calculated we can turn to the evaluation of the treamer integrals. This is done by running the
Charged Particle Tracingthis node we define the
Charged Particle Tracingoriginally intended for calculating trajectories of moving charged partimagnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node Charged Particle Tracing
Particle Propertiesformulation.
The particle tracing procedure starts by selecting those surfaces from which the field lines are starting. This is done under the node. Also, the number of field lines ("particles") is entered. Preferably one selects all sureither high or zero potential in order to make sure that all field lines are included in the
The general structure of the model displayed in the Model Builder
d is found as is shown in Fig. 3Note the regions where value 2.6 kV/mm required for net charge
Once the background electric field is calculated we can turn to the evaluation of the
This is done by running the Charged Particle Tracingthis node we define the subnodes
Charged Particle Tracingoriginally intended for calculating trajectories of moving charged particles in electric and/or magnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node Charged Particle Tracing
Particle Propertiesformulation.
The particle tracing procedure starts by selecting those surfaces from which the field lines are starting. This is done under the node. Also, the number of field lines ("particles") is entered. Preferably one selects all sureither high or zero potential in order to make sure that all field lines are included in the
The general structure of the model displayed in the Model Builder.
d is found as is shown in Fig. 3Note the regions where E value 2.6 kV/mm required for net charge
Once the background electric field is calculated we can turn to the evaluation of the
This is done by running the Charged Particle Tracing problem in Study 2. In
subnodes
Charged Particle Tracingoriginally intended for calculating trajectories of
cles in electric and/or magnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node Charged Particle Tracing (cpt)
Particle Properties
The particle tracing procedure starts by selecting those surfaces from which the field lines are starting. This is done under the node. Also, the number of field lines ("particles") is entered. Preferably one selects all sureither high or zero potential in order to make sure that all field lines are included in the
The general structure of the model
d is found as is shown in Fig. 3 exceeds the critical
value 2.6 kV/mm required for net charge
Once the background electric field is calculated we can turn to the evaluation of the
This is done by running the problem in Study 2. In
subnodes
Charged Particle Tracingoriginally intended for calculating trajectories of
cles in electric and/or magnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node
(cpt)Particle Properties
The particle tracing procedure starts by selecting those surfaces from which the field lines are starting. This is done under the node. Also, the number of field lines ("particles") is entered. Preferably one selects all sureither high or zero potential in order to make sure that all field lines are included in the
The general structure of the model
d is found as is shown in Fig. 3exceeds the critical
value 2.6 kV/mm required for net charge
Once the background electric field is calculated we can turn to the evaluation of the
This is done by running the problem in Study 2. In
subnodes shown in
Charged Particle Tracingoriginally intended for calculating trajectories of
cles in electric and/or magnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node
(cpt)) one can in fact Particle Properties
The particle tracing procedure starts by selecting those surfaces from which the field lines are starting. This is done under the node. Also, the number of field lines ("particles") is entered. Preferably one selects all sureither high or zero potential in order to make sure that all field lines are included in the
The general structure of the model
d is found as is shown in Fig. 3exceeds the critical
value 2.6 kV/mm required for net charge
Once the background electric field is calculated we can turn to the evaluation of the
This is done by running the problem in Study 2. In
shown in
Charged Particle Tracing originally intended for calculating trajectories of
cles in electric and/or magnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node
one can in fact choose
The particle tracing procedure starts by selecting those surfaces from which the field lines are starting. This is done under the node. Also, the number of field lines ("particles") is entered. Preferably one selects all sureither high or zero potential in order to make sure that all field lines are included in the
The general structure of the model
d is found as is shown in Fig. 3exceeds the critical
value 2.6 kV/mm required for net charge
Once the background electric field is calculated we can turn to the evaluation of the
This is done by running the problem in Study 2. In
shown in
feature is originally intended for calculating trajectories of
cles in electric and/or magnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node
one can in fact choose
The particle tracing procedure starts by selecting those surfaces from which the field lines are starting. This is done under the node. Also, the number of field lines ("particles") is entered. Preferably one selects all surfaces at either high or zero potential in order to make sure that all field lines are included in the
The general structure of the model
d is found as is shown in Fig. 3exceeds the critical
value 2.6 kV/mm required for net charge
Once the background electric field is calculated we can turn to the evaluation of the
This is done by running the problem in Study 2. In
shown in Fig.
feature is originally intended for calculating trajectories of
cles in electric and/or magnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node
one can in fact choose
The particle tracing procedure starts by selecting those surfaces from which the field lines are starting. This is done under the Inletnode. Also, the number of field lines ("particles")
faces at either high or zero potential in order to make sure that all field lines are included in the
The general structure of the model
d is found as is shown in Fig. 3. exceeds the critical
value 2.6 kV/mm required for net charge
Once the background electric field is calculated we can turn to the evaluation of the
This is done by running the problem in Study 2. In
Fig.
feature is originally intended for calculating trajectories of
cles in electric and/or magnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node
one can in fact choose the
The particle tracing procedure starts by selecting those surfaces from which the field
Inletnode. Also, the number of field lines ("particles")
faces at either high or zero potential in order to make sure that all field lines are included in the
The general structure of the model
. exceeds the critical
value 2.6 kV/mm required for net charge
Once the background electric field is calculated we can turn to the evaluation of the
This is done by running the problem in Study 2. In
Fig.
feature is originally intended for calculating trajectories of
cles in electric and/or magnetic fields. However, electric field lines can be identified as the trajectories of charged particles having zero mass. Under the top node
one can in fact the
The particle tracing procedure starts by selecting those surfaces from which the field
Inlet node. Also, the number of field lines ("particles")
faces at either high or zero potential in order to make sure that all field lines are included in the
conductor and grounded wallboundaries of regions where with grey curves.
"particles" under the we want the particle trajectories to be identical to the field lines we should define the velocity as being parallel to the normalized field in the definition of according to velocity of the order of 1 m/s, and knowing the typical distances between positive and negative electrodes, one can easily estimate therequired for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the opposite wall. Under the the wall condition particle does not bouncvolume.
we then define the required integrals along each field line. This is done by introducing
Particle Tracing
Figure
conductor and grounded wallboundaries of regions where with grey curves.
The n
"particles" under the we want the particle trajectories to be identical to the field lines we should define the velocity as being parallel to the normalized field in the definition of according to velocity of the order of 1 m/s, and knowing the typical distances between positive and negative electrodes, one can easily estimate therequired for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the opposite wall. Under the the wall condition particle does not bouncvolume.
Under the we then define the required integrals along each field line. This is done by introducing
Figure
Particle Tracing
Figure
conductor and grounded wallboundaries of regions where with grey curves.
The n
"particles" under the we want the particle trajectories to be identical to the field lines we should define the velocity as being parallel to the normalized field in the definition of according to velocity of the order of 1 m/s, and knowing the typical distances between positive and negative electrodes, one can easily estimate therequired for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the opposite wall. Under the the wall condition particle does not bouncvolume.
Under the we then define the required integrals along each field line. This is done by introducing
Figure
Particle Tracing
Figure conductor and grounded wallboundaries of regions where with grey curves.
The next step is to define the velocity of the "particles" under the we want the particle trajectories to be identical to the field lines we should define the velocity as being parallel to the normalized field in the definition of according to velocity of the order of 1 m/s, and knowing the typical distances between positive and negative electrodes, one can easily estimate therequired for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the opposite wall. Under the the wall condition particle does not bouncvolume.
Under the we then define the required integrals along each field line. This is done by introducing
Figure Particle Tracing
Figure 3. conductor and grounded wallboundaries of regions where with grey curves.
ext step is to define the velocity of the "particles" under the we want the particle trajectories to be identical to the field lines we should define the velocity as being parallel to the normalized field in the definition of according to velocity of the order of 1 m/s, and knowing the typical distances between positive and negative electrodes, one can easily estimate therequired for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the opposite wall. Under the the wall condition particle does not bounc
Under the we then define the required integrals along each field line. This is done by introducing
Figure 4. Particle Tracing
. Electric field between high voltageconductor and grounded wallboundaries of regions where with grey curves.
ext step is to define the velocity of the "particles" under the we want the particle trajectories to be identical to the field lines we should define the velocity as being parallel to Ethe normalized field in the definition of
=velocity of the order of 1 m/s, and knowing the typical distances between positive and negative electrodes, one can easily estimate therequired for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the opposite wall. Under the the wall condition particle does not bounc
Under the Charged Particle Tracingwe then define the required integrals along each field line. This is done by introducing
. Definitions made in the Particle Tracing node
Electric field between high voltageconductor and grounded wallboundaries of regions where
ext step is to define the velocity of the "particles" under the Particle Propertieswe want the particle trajectories to be identical to the field lines we should define the velocity as
E. Here it is convenient to use the normalized field in the definition of
/|velocity of the order of 1 m/s, and knowing the typical distances between positive and negative electrodes, one can easily estimate therequired for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the opposite wall. Under the the wall condition Freezeparticle does not bounc
Charged Particle Tracingwe then define the required integrals along each field line. This is done by introducing
Definitions made in the node.
Electric field between high voltageconductor and grounded wallboundaries of regions where
ext step is to define the velocity of the Particle Properties
we want the particle trajectories to be identical to the field lines we should define the velocity as
. Here it is convenient to use the normalized field in the definition of
| |, see Fig. velocity of the order of 1 m/s, and knowing the typical distances between positive and negative electrodes, one can easily estimate therequired for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the opposite wall. Under the
Freezeparticle does not bounc
Charged Particle Tracingwe then define the required integrals along each field line. This is done by introducing
Definitions made in the
Electric field between high voltageconductor and grounded wall. boundaries of regions where
ext step is to define the velocity of the Particle Properties
we want the particle trajectories to be identical to the field lines we should define the velocity as
. Here it is convenient to use the normalized field in the definition of
, see Fig. velocity of the order of 1 m/s, and knowing the typical distances between positive and negative electrodes, one can easily estimate therequired for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the opposite wall. Under the Wall
Freeze to make sure that the particle does not bounce back into the gas
Charged Particle Tracingwe then define the required integrals along each field line. This is done by introducing
Definitions made in the
Electric field between high voltage Field lines in red and
eff (
ext step is to define the velocity of the Particle Properties
we want the particle trajectories to be identical to the field lines we should define the velocity as
. Here it is convenient to use the normalized field in the definition of
, see Fig. velocity of the order of 1 m/s, and knowing the typical distances between positive and negative electrodes, one can easily estimate therequired for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the
Wallto make sure that the
e back into the gas
Charged Particle Tracingwe then define the required integrals along each field line. This is done by introducing
Definitions made in the
Electric field between high voltageField lines in red and
(E) > 0 are marked
ext step is to define the velocity of the Particle Properties
we want the particle trajectories to be identical to the field lines we should define the velocity as
. Here it is convenient to use the normalized field in the definition of
, see Fig. velocity of the order of 1 m/s, and knowing the typical distances between positive and negative electrodes, one can easily estimate therequired for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the
Wall node we choose to make sure that the
e back into the gas
Charged Particle Tracingwe then define the required integrals along each field line. This is done by introducing
Definitions made in the
Electric field between high voltageField lines in red and
) > 0 are marked
ext step is to define the velocity of the Particle Properties
we want the particle trajectories to be identical to the field lines we should define the velocity as
. Here it is convenient to use the normalized field in the definition of
, see Fig. 5. Bvelocity of the order of 1 m/s, and knowing the typical distances between positive and negative electrodes, one can easily estimate therequired for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the
node we choose to make sure that the
e back into the gas
Charged Particle Tracingwe then define the required integrals along each field line. This is done by introducing Auxiliary
Definitions made in the
Electric field between high voltageField lines in red and
) > 0 are marked
ext step is to define the velocity of the Particle Properties node.
we want the particle trajectories to be identical to the field lines we should define the velocity as
. Here it is convenient to use the normalized field in the definition of
By using a velocity of the order of 1 m/s, and knowing the typical distances between positive and negative electrodes, one can easily estimate therequired for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the
node we choose to make sure that the
e back into the gas
Charged Particle Tracingwe then define the required integrals along each
Auxiliary
Definitions made in the Charged
Electric field between high voltageField lines in red and
) > 0 are marked
ext step is to define the velocity of the node.
we want the particle trajectories to be identical to the field lines we should define the velocity as
. Here it is convenient to use the normalized field in the definition of
y using a velocity of the order of 1 m/s, and knowing the typical distances between positive and negative electrodes, one can easily estimate the time required for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the
node we choose to make sure that the
e back into the gas
Charged Particle Tracing node, we then define the required integrals along each
Auxiliary
Charged
Electric field between high voltageField lines in red and
) > 0 are marked
ext step is to define the velocity of the node. If
we want the particle trajectories to be identical to the field lines we should define the velocity as
. Here it is convenient to use the normalized field in the definition of v
y using a velocity of the order of 1 m/s, and knowing the typical distances between positive and negative
time required for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the
node we choose to make sure that the
e back into the gas
node, we then define the required integrals along each
Auxiliary
Charged
Electric field between high voltage Field lines in red and
) > 0 are marked
ext step is to define the velocity of the If
we want the particle trajectories to be identical to the field lines we should define the velocity as
. Here it is convenient to use v
y using a velocity of the order of 1 m/s, and knowing the typical distances between positive and negative
time required for a "particle" to reach the opposite electrode. One also has to determine what happens to a "particle" once it reaches the
node we choose to make sure that the
e back into the gas
node, we then define the required integrals along each
Charged
made in the
Dependent Variableswant to calculate, see Fig. 4.
Auxiliary Dependent Variablesthe field line length integral having different streamer integrals for streamers emerging from the positive electrode and one for streamers starting at the negative electrcorresponding to the positive electrode the integrand which is 1 when positive electrode and 0 when other integral is defined in an analogous way for the definitions we can separate between streamers starting from either the positive or the negative electrode.
a time dependent simulation, solving for the Charged Particle TrFig. 6some final time t_endwhere |v
4.
streamer integrals computed, it remains to present the result in an informative and easily understandable way.
corresponding to regielectrodes cana net electron production close to the positive electrode is shown while those close to the negative
Figure made in the
Dependent Variableswant to calculate, see Fig. 4.
The integrand is called Auxiliary Dependent Variablesthe field line length integral having different streamer integrals for streamers emerging from the positive electrode and one for streamers starting at the negative electrcorresponding to the positive electrode the integrand which is 1 when positive electrode and 0 when other integral is defined in an analogous way for the definitions we can separate between streamers starting from either the positive or the negative electrode.
The final step consists of running Study 2 as a time dependent simulation, solving for the Charged Particle TrFig. 6some final time t_endwhere v| ~ 1 is the normalized velocity
. Post processing
Now when we have the solution and the streamer integrals computed, it remains to present the result in an informative and easily understandable way.
First, the corresponding to regielectrodes cana net electron production close to the positive electrode is shown while those close to the negative
Figure made in the
Dependent Variableswant to calculate, see Fig. 4.
The integrand is called Auxiliary Dependent Variablesthe field line length integral having different streamer integrals for streamers emerging from the positive electrode and one for streamers starting at the negative electrcorresponding to the positive electrode the integrand which is 1 when positive electrode and 0 when other integral is defined in an analogous way for the negative electrode. According to these definitions we can separate between streamers starting from either the positive or the negative electrode.
The final step consists of running Study 2 as a time dependent simulation, solving for the Charged Particle TrFig. 6. The integration is performed from some final time t_end can easily be estimated as where D
~ 1 is the normalized velocity
Post processing
Now when we have the solution and the streamer integrals computed, it remains to present the result in an informative and easily understandable way.
First, the corresponding to regielectrodes cana net electron production close to the positive electrode is shown while those close to the negative
Figure 5made in the Particle Properties
Dependent Variableswant to calculate, see Fig. 4.
The integrand is called Auxiliary Dependent Variablesthe field line length integral having different streamer integrals for streamers emerging from the positive electrode and one for streamers starting at the negative electrcorresponding to the positive electrode the integrand which is 1 when positive electrode and 0 when other integral is defined in an analogous way for
negative electrode. According to these definitions we can separate between streamers starting from either the positive or the negative electrode.
The final step consists of running Study 2 as a time dependent simulation, solving for the Charged Particle Tr
. The integration is performed from some final time
can easily be estimated as D is the dimension of the object and
~ 1 is the normalized velocity
Post processing
Now when we have the solution and the streamer integrals computed, it remains to present the result in an informative and easily understandable way.
First, the corresponding to regielectrodes cana net electron production close to the positive electrode is shown while those close to the negative electrode can be seen in Fig. 8
5. Definitions of the normalized velocity Particle Properties
Dependent Variableswant to calculate, see Fig. 4.
The integrand is called Auxiliary Dependent Variablesthe field line length integral having different streamer integrals for streamers emerging from the positive electrode and one for streamers starting at the negative electrcorresponding to the positive electrode the
eff which is 1 when positive electrode and 0 when other integral is defined in an analogous way for
negative electrode. According to these definitions we can separate between streamers starting from either the positive or the negative
The final step consists of running Study 2 as a time dependent simulation, solving for the Charged Particle Tr
. The integration is performed from some final time
can easily be estimated as is the dimension of the object and
~ 1 is the normalized velocity
Post processing
Now when we have the solution and the streamer integrals computed, it remains to present the result in an informative and easily understandable way.
First, the effective ionization function corresponding to regielectrodes can a net electron production close to the positive electrode is shown while those close to the
electrode can be seen in Fig. 8
Definitions of the normalized velocity Particle Properties
Dependent Variableswant to calculate, see Fig. 4.
The integrand is called Auxiliary Dependent Variablesthe field line length integral having Rdifferent streamer integrals for streamers emerging from the positive electrode and one for streamers starting at the negative electrode. For the integral corresponding to the positive electrode the
(E) which is 1 when positive electrode and 0 when other integral is defined in an analogous way for
negative electrode. According to these definitions we can separate between streamers starting from either the positive or the negative
The final step consists of running Study 2 as a time dependent simulation, solving for the Charged Particle Tr
. The integration is performed from some final time t =
can easily be estimated as is the dimension of the object and
~ 1 is the normalized velocity
Post processing
Now when we have the solution and the streamer integrals computed, it remains to present the result in an informative and easily understandable way.
effective ionization function corresponding to regi
be plotted. In Fig. 7a net electron production close to the positive electrode is shown while those close to the
electrode can be seen in Fig. 8
Definitions of the normalized velocity Particle Properties
Dependent Variables, one for each integral we want to calculate, see Fig. 4.
The integrand is called Auxiliary Dependent Variablesthe field line length
R = 1. different streamer integrals for streamers emerging from the positive electrode and one for streamers starting at the
ode. For the integral corresponding to the positive electrode the
) is multiplied with a factor which is 1 when E positive electrode and 0 when other integral is defined in an analogous way for
negative electrode. According to these definitions we can separate between streamers starting from either the positive or the negative
The final step consists of running Study 2 as a time dependent simulation, solving for the Charged Particle Tr
. The integration is performed from = t_end
can easily be estimated as is the dimension of the object and
~ 1 is the normalized velocity
Post processing
Now when we have the solution and the streamer integrals computed, it remains to present the result in an informative and easily understandable way.
effective ionization function corresponding to regi
be plotted. In Fig. 7a net electron production close to the positive electrode is shown while those close to the
electrode can be seen in Fig. 8
Definitions of the normalized velocity Particle Properties
, one for each integral we want to calculate, see Fig. 4.
The integrand is called Auxiliary Dependent Variablesthe field line length L
= 1. different streamer integrals for streamers emerging from the positive electrode and one for streamers starting at the
ode. For the integral corresponding to the positive electrode the
is multiplied with a factor decreases away from the
positive electrode and 0 when other integral is defined in an analogous way for
negative electrode. According to these definitions we can separate between streamers starting from either the positive or the negative
The final step consists of running Study 2 as a time dependent simulation, solving for the Charged Particle Tracing
. The integration is performed from t_end
can easily be estimated as is the dimension of the object and
~ 1 is the normalized velocity
Now when we have the solution and the streamer integrals computed, it remains to present the result in an informative and easily
effective ionization function corresponding to regions close to the two
be plotted. In Fig. 7a net electron production close to the positive electrode is shown while those close to the
electrode can be seen in Fig. 8
Definitions of the normalized velocity Particle Properties
, one for each integral we want to calculate, see Fig. 4.
The integrand is called Auxiliary Dependent Variables
is give= 1. Then we define two
different streamer integrals Sfor streamers emerging from the positive electrode and one for streamers starting at the
ode. For the integral corresponding to the positive electrode the
is multiplied with a factor decreases away from the
positive electrode and 0 when other integral is defined in an analogous way for
negative electrode. According to these definitions we can separate between streamers starting from either the positive or the negative
The final step consists of running Study 2 as a time dependent simulation, solving for the
acing . The integration is performed from
t_end. A reasonable value for can easily be estimated as
is the dimension of the object and ~ 1 is the normalized velocity
Now when we have the solution and the streamer integrals computed, it remains to present the result in an informative and easily
effective ionization function ons close to the two
be plotted. In Fig. 7a net electron production close to the positive electrode is shown while those close to the
electrode can be seen in Fig. 8
Definitions of the normalized velocity node
, one for each integral we
The integrand is called Source RAuxiliary Dependent Variables
is giveThen we define two
S given by (1): One for streamers emerging from the positive electrode and one for streamers starting at the
ode. For the integral corresponding to the positive electrode the
is multiplied with a factor decreases away from the
positive electrode and 0 when other integral is defined in an analogous way for
negative electrode. According to these definitions we can separate between streamers starting from either the positive or the negative
The final step consists of running Study 2 as a time dependent simulation, solving for the
variables only, see . The integration is performed from
. A reasonable value for can easily be estimated as
is the dimension of the object and ~ 1 is the normalized velocity
Now when we have the solution and the streamer integrals computed, it remains to present the result in an informative and easily
effective ionization function ons close to the two
be plotted. In Fig. 7a net electron production close to the positive electrode is shown while those close to the
electrode can be seen in Fig. 8
Definitions of the normalized velocity node.
, one for each integral we
Source RAuxiliary Dependent Variables heading. First,
is given Then we define two
given by (1): One for streamers emerging from the positive electrode and one for streamers starting at the
ode. For the integral corresponding to the positive electrode the
is multiplied with a factor decreases away from the
positive electrode and 0 when E increases. The other integral is defined in an analogous way for
negative electrode. According to these definitions we can separate between streamers starting from either the positive or the negative
The final step consists of running Study 2 as a time dependent simulation, solving for the
variables only, see . The integration is performed from
. A reasonable value for can easily be estimated as
is the dimension of the object and ~ 1 is the normalized velocity that is used.
Now when we have the solution and the streamer integrals computed, it remains to present the result in an informative and easily
effective ionization function ons close to the two
be plotted. In Fig. 7 a net electron production close to the positive electrode is shown while those close to the
electrode can be seen in Fig. 8
Definitions of the normalized velocity
, one for each integral we
Source R heading. First, by such an
Then we define two given by (1): One
for streamers emerging from the positive electrode and one for streamers starting at the
ode. For the integral corresponding to the positive electrode the
is multiplied with a factor decreases away from the
increases. The other integral is defined in an analogous way for
negative electrode. According to these definitions we can separate between streamers starting from either the positive or the negative
The final step consists of running Study 2 as a time dependent simulation, solving for the
variables only, see . The integration is performed from
. A reasonable value for can easily be estimated as t_end
is the dimension of the object and that is used.
Now when we have the solution and the streamer integrals computed, it remains to present the result in an informative and easily
effective ionization function ons close to the two
the areaa net electron production close to the positive electrode is shown while those close to the
electrode can be seen in Fig. 8
Definitions of the normalized velocity
, one for each integral we
under the heading. First,
by such an Then we define two
given by (1): One for streamers emerging from the positive electrode and one for streamers starting at the
ode. For the integral corresponding to the positive electrode the
is multiplied with a factor decreases away from the
increases. The other integral is defined in an analogous way for
negative electrode. According to these definitions we can separate between streamers starting from either the positive or the negative
The final step consists of running Study 2 as a time dependent simulation, solving for the
variables only, see . The integration is performed from t
. A reasonable value for t_end
is the dimension of the object and that is used.
Now when we have the solution and the streamer integrals computed, it remains to present the result in an informative and easily
effective ionization function ons close to the two
the areaa net electron production close to the positive electrode is shown while those close to the
electrode can be seen in Fig. 8.
Definitions of the normalized velocity
, one for each integral we
under the heading. First,
by such an Then we define two
given by (1): One for streamers emerging from the positive electrode and one for streamers starting at the
ode. For the integral corresponding to the positive electrode the
is multiplied with a factor decreases away from the
increases. The other integral is defined in an analogous way for
negative electrode. According to these definitions we can separate between streamers starting from either the positive or the negative
The final step consists of running Study 2 as a time dependent simulation, solving for the
variables only, see t = 0 to
. A reasonable value for t_end = D
is the dimension of the object and that is used.
Now when we have the solution and the streamer integrals computed, it remains to present the result in an informative and easily
effective ionization function eff ons close to the two
the area with a net electron production close to the positive electrode is shown while those close to the
Definitions of the normalized velocity
, one for each integral we
under the heading. First,
by such an Then we define two
given by (1): One for streamers emerging from the positive electrode and one for streamers starting at the
ode. For the integral corresponding to the positive electrode the
is multiplied with a factor decreases away from the
increases. The other integral is defined in an analogous way for
negative electrode. According to these definitions we can separate between streamers starting from either the positive or the negative
The final step consists of running Study 2 as a time dependent simulation, solving for the
variables only, see = 0 to
. A reasonable value for D/v,
is the dimension of the object and v =
Now when we have the solution and the streamer integrals computed, it remains to present the result in an informative and easily
eff (E) ons close to the two
with a net electron production close to the positive electrode is shown while those close to the
Definitions of the normalized velocity
, one for each integral we
under the heading. First,
by such an Then we define two
given by (1): One for streamers emerging from the positive electrode and one for streamers starting at the
ode. For the integral corresponding to the positive electrode the
is multiplied with a factor decreases away from the
increases. The other integral is defined in an analogous way for
negative electrode. According to these definitions we can separate between streamers starting from either the positive or the negative
The final step consists of running Study 2 as a time dependent simulation, solving for the
variables only, see = 0 to
. A reasonable value for ,
=
Now when we have the solution and the streamer integrals computed, it remains to present the result in an informative and easily
) ons close to the two
with a net electron production close to the positive electrode is shown while those close to the
time stepping in Study 2
the regions with net electron production are located and hence where we discharges to be initiated.
electron prelectrode
Figure
time stepping in Study 2
From Figures 7 and 8the regions with net electron production are located and hence where we discharges to be initiated.
Figure
electron prelectrode
Figure
time stepping in Study 2
From Figures 7 and 8the regions with net electron production are located and hence where we discharges to be initiated.
Figure
electron prelectrode
Figure 6time stepping in Study 2
From Figures 7 and 8the regions with net electron production are located and hence where we discharges to be initiated.
Figure electron production electrode.
6. Settings for running the time stepping in Study 2
From Figures 7 and 8the regions with net electron production are located and hence where we discharges to be initiated.
Figure 7. oduction
Settings for running the time stepping in Study 2
From Figures 7 and 8the regions with net electron production are located and hence where we discharges to be initiated.
. The region having a positive net oduction
Settings for running the time stepping in Study 2
From Figures 7 and 8the regions with net electron production are located and hence where we discharges to be initiated.
The region having a positive net oduction eff
Settings for running the time stepping in Study 2.
From Figures 7 and 8the regions with net electron production are located and hence where we discharges to be initiated.
The region having a positive net eff (E) > 0 close
Settings for running the
From Figures 7 and 8 we now know where
the regions with net electron production are located and hence where we discharges to be initiated.
The region having a positive net ) > 0 close
Settings for running the
we now know where the regions with net electron production are located and hence where we
The region having a positive net ) > 0 close
Settings for running the
we now know where the regions with net electron production are located and hence where we
The region having a positive net ) > 0 close
Settings for running the particle tracing
we now know where the regions with net electron production are located and hence where we might
The region having a positive net ) > 0 close to the positive
particle tracing
we now know where the regions with net electron production are
might
The region having a positive net to the positive
particle tracing
we now know where the regions with net electron production are
expect
The region having a positive net to the positive
particle tracing
we now know where the regions with net electron production are
expect
The region having a positive net to the positive
particle tracing
we now know where the regions with net electron production are
expect
The region having a positive net to the positive
electron production electrode
for streamer inceptionaddition, the criteriabreakdown across the gap is to be expected.
to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral S within the region having net charge production.
inception condition (1) for discharges starting from the positive electrode.color coded.
Figure
electron production electrode
For this to happen
for streamer inceptionaddition, the criteriabreakdown across the gap is to be expected.
Figure 9to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral
is color coded and the lines are only shown within the region having net charge production.
Figure
inception condition (1) for discharges starting from the positive electrode.color coded.
Figure electron production electrode
For this to happenfor streamer inceptionaddition, the criteriabreakdown across the gap is to be expected.
Figure 9to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral
is color coded and the lines are only shown within the region having net charge production.
Figure
inception condition (1) for discharges starting from the positive electrode.color coded.
Figure electron production electrode.
For this to happenfor streamer inceptionaddition, the criteriabreakdown across the gap is to be expected.
Figure 9to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral
is color coded and the lines are only shown within the region having net charge production.
Figure inception condition (1) for discharges starting from the positive electrode.color coded.
Figure 8. The regionelectron production
For this to happenfor streamer inceptionaddition, the criteriabreakdown across the gap is to be expected.
Figure 9 shows the field lines that correspond to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral
is color coded and the lines are only shown within the region having net charge production.
Figure 9. inception condition (1) for discharges starting from the positive electrode.
The regionelectron production
For this to happenfor streamer inceptionaddition, the criteriabreakdown across the gap is to be expected.
shows the field lines that correspond to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral
is color coded and the lines are only shown within the region having net charge production.
Field lines satisfying the streamer inception condition (1) for discharges starting from the positive electrode. Magnitude of streamer integral
The regionelectron production eff
For this to happenfor streamer inceptionaddition, the criteriabreakdown across the gap is to be expected.
shows the field lines that correspond to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral
is color coded and the lines are only shown within the region having net charge production.
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Magnitude of streamer integral
The regioneff (E) > 0 close
For this to happen, however, for streamer inception hasaddition, the criteria (2) breakdown across the gap is to be expected.
shows the field lines that correspond to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral
is color coded and the lines are only shown within the region having net charge production.
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Magnitude of streamer integral
The regions having a positive net ) > 0 close
, however, has
(2) must be satisfied if breakdown across the gap is to be expected.
shows the field lines that correspond to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral
is color coded and the lines are only shown within the region having net charge production.
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Magnitude of streamer integral
having a positive net ) > 0 close
, however, to be fulfilled. In
must be satisfied if breakdown across the gap is to be expected.
shows the field lines that correspond to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral
is color coded and the lines are only shown within the region having net charge production.
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Magnitude of streamer integral
having a positive net ) > 0 close
, however, the to be fulfilled. In
must be satisfied if breakdown across the gap is to be expected.
shows the field lines that correspond to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral
is color coded and the lines are only shown within the region having net charge production.
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Magnitude of streamer integral
having a positive net to the
the criteria (1) to be fulfilled. In
must be satisfied if breakdown across the gap is to be expected.
shows the field lines that correspond to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral
is color coded and the lines are only shown within the region having net charge production.
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Magnitude of streamer integral
having a positive net to the negative
criteria (1) to be fulfilled. In
must be satisfied if breakdown across the gap is to be expected.
shows the field lines that correspond to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral
is color coded and the lines are only shown within the region having net charge production.
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Magnitude of streamer integral
having a positive net negative
criteria (1) to be fulfilled. In
must be satisfied if breakdown across the gap is to be expected.
shows the field lines that correspond to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral
is color coded and the lines are only shown within the region having net charge production.
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Magnitude of streamer integral
having a positive net negative
criteria (1) to be fulfilled. In
must be satisfied if
shows the field lines that correspond to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral
is color coded and the lines are only shown within the region having net charge production.
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Magnitude of streamer integral S is
having a positive net negative
criteria (1) to be fulfilled. In
must be satisfied if
shows the field lines that correspond to streamers starting from the positive electrode and satisfying (1). The magnitude of the integral
is color coded and the lines are only shown
Field lines satisfying the streamer inception condition (1) for discharges starting from the
is
propagation condition (2) for discharges the positive electrode. It is interesting to observe that streamers are not initiated at all points on the electrode surface where the electric field exceeds the cri2.6 kV/mm. In Fig. 10corresponding field lines whiccondition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for discharges starting at the negative ebe seen in Figs. 11 and 12
inception condition (1) for discharges starting from the negative electrode.
Figure
propagation condition (2) for discharges the positive electrode. It is interesting to observe that streamers are not initiated at all points on the electrode surface where the electric field exceeds the cri2.6 kV/mm. In Fig. 10corresponding field lines whiccondition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for discharges starting at the negative ebe seen in Figs. 11 and 12
Figure inception condition (1) for discharges starting from the negative electrode.
Figure
propagation condition (2) for discharges the positive electrode.
It is interesting to observe that streamers are not initiated at all points on the electrode surface where the electric field exceeds the cri2.6 kV/mm. In Fig. 10corresponding field lines whiccondition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for discharges starting at the negative ebe seen in Figs. 11 and 12
Figure inception condition (1) for discharges starting from the negative electrode.
Figure propagation condition (2) for discharges the positive electrode.
It is interesting to observe that streamers are not initiated at all points on the electrode surface where the electric field exceeds the cri2.6 kV/mm. In Fig. 10corresponding field lines whiccondition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for discharges starting at the negative ebe seen in Figs. 11 and 12
Figure inception condition (1) for discharges starting from the negative electrode.
Figure 10. propagation condition (2) for discharges the positive electrode.
It is interesting to observe that streamers are not initiated at all points on the electrode surface where the electric field exceeds the cri2.6 kV/mm. In Fig. 10corresponding field lines whiccondition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for discharges starting at the negative ebe seen in Figs. 11 and 12
Figure 11. inception condition (1) for discharges starting from the negative electrode.
. Field lines satisfying the streamer propagation condition (2) for discharges the positive electrode.
It is interesting to observe that streamers are not initiated at all points on the electrode surface where the electric field exceeds the cri2.6 kV/mm. In Fig. 10corresponding field lines whiccondition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for discharges starting at the negative ebe seen in Figs. 11 and 12
. Field lines satisfying the streamer inception condition (1) for discharges starting from the negative electrode.
Field lines satisfying the streamer propagation condition (2) for discharges the positive electrode.
It is interesting to observe that streamers are not initiated at all points on the electrode surface where the electric field exceeds the cri2.6 kV/mm. In Fig. 10corresponding field lines whiccondition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for discharges starting at the negative ebe seen in Figs. 11 and 12
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Field lines satisfying the streamer propagation condition (2) for discharges
It is interesting to observe that streamers are not initiated at all points on the electrode surface where the electric field exceeds the cri2.6 kV/mm. In Fig. 10corresponding field lines whiccondition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for discharges starting at the negative ebe seen in Figs. 11 and 12
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Field lines satisfying the streamer propagation condition (2) for discharges
It is interesting to observe that streamers are not initiated at all points on the electrode surface where the electric field exceeds the cri2.6 kV/mm. In Fig. 10corresponding field lines whiccondition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for discharges starting at the negative ebe seen in Figs. 11 and 12.
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Field lines satisfying the streamer propagation condition (2) for discharges
It is interesting to observe that streamers are not initiated at all points on the electrode surface where the electric field exceeds the cri2.6 kV/mm. In Fig. 10 corresponding field lines whiccondition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for discharges starting at the negative e
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Field lines satisfying the streamer propagation condition (2) for discharges
It is interesting to observe that streamers are not initiated at all points on the electrode surface where the electric field exceeds the cri
is shown the corresponding field lines which satisfy the condition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for discharges starting at the negative e
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Field lines satisfying the streamer propagation condition (2) for discharges starting from
It is interesting to observe that streamers are not initiated at all points on the electrode surface where the electric field exceeds the cri
is shown the h satisfy the
condition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for discharges starting at the negative electrode can
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Field lines satisfying the streamer starting from
It is interesting to observe that streamers are not initiated at all points on the electrode surface where the electric field exceeds the critical value
is shown the h satisfy the
condition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for
lectrode can
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Field lines satisfying the streamer starting from
It is interesting to observe that streamers are not initiated at all points on the electrode surface
tical value is shown the
h satisfy the condition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for
lectrode can
Field lines satisfying the streamer inception condition (1) for discharges starting from the
Field lines satisfying the streamer starting from
It is interesting to observe that streamers are not initiated at all points on the electrode surface
tical value is shown the
h satisfy the condition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for
lectrode can
Field lines satisfying the streamer
inception condition (1) for discharges starting from the
Field lines satisfying the streamer starting from
It is interesting to observe that streamers are not initiated at all points on the electrode surface
tical value is shown the
h satisfy the condition (2) for breakdown across the gap. Note that in this case all field lines that satisfy (1) also fulfill (2). Finally, a similar pair of figures for
lectrode can
Field lines satisfying the streamer inception condition (1) for discharges starting from the
propagation condition (2) for discharges starting from the negative electrode.
5.
well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in order to element, a block protruding from the inner high voltageelectric field is solved for and the particle tracing is carried out generating 1000 field lanalyze as is seen in Fig. post processing can be employed as for the 2D case shown earlier. As Fig. 15from the positive to the negative electrode.
Figure propagation condition (2) for discharges starting from the negative electrode.
. A
As demonstrated above, the method works
well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in order to element, a block protruding from the inner high voltageelectric field is solved for and the particle tracing is carried out generating 1000 field lanalyze as is seen in Fig. post processing can be employed as for the 2D case shown earlier. As Fig. 15from the positive to the negative electrode.
Figure
Figure propagation condition (2) for discharges starting from the negative electrode.
A 3D example
As demonstrated above, the method works well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in order to element, a block protruding from the inner high voltage electric field is solved for and the particle tracing is carried out generating 1000 field lanalyze as is seen in Fig. post processing can be employed as for the 2D case shown earlier. As Fig. 15 from the positive to the negative electrode.
Figure
Figure 1propagation condition (2) for discharges starting from the negative electrode.
3D example
As demonstrated above, the method works well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in order to introduce a truly three dimensional element, a block protruding from the inner high
conductor is added, see Fig. 13electric field is solved for and the particle tracing is carried out generating 1000 field lanalyze as is seen in Fig. post processing can be employed as for the 2D case shown earlier. As
the field lines giving rise to a flashover from the positive to the negative electrode.
Figure 1
12. propagation condition (2) for discharges starting from the negative electrode.
3D example
As demonstrated above, the method works well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in
introduce a truly three dimensional element, a block protruding from the inner high
conductor is added, see Fig. 13electric field is solved for and the particle tracing is carried out generating 1000 field lanalyze as is seen in Fig. post processing can be employed as for the 2D case shown earlier. As
the field lines giving rise to a flashover from the positive to the negative electrode.
13. 3D geometry used in the simul
. Field lines satisfying the streamer propagation condition (2) for discharges starting from the negative electrode.
3D example
As demonstrated above, the method works well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in
introduce a truly three dimensional element, a block protruding from the inner high
conductor is added, see Fig. 13electric field is solved for and the particle tracing is carried out generating 1000 field lanalyze as is seen in Fig. post processing can be employed as for the 2D case shown earlier. As
the field lines giving rise to a flashover from the positive to the negative electrode.
3D geometry used in the simul
Field lines satisfying the streamer propagation condition (2) for discharges starting from the negative electrode.
3D example
As demonstrated above, the method works well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in
introduce a truly three dimensional element, a block protruding from the inner high
conductor is added, see Fig. 13electric field is solved for and the particle tracing is carried out generating 1000 field lanalyze as is seen in Fig. post processing can be employed as for the 2D case shown earlier. As
the field lines giving rise to a flashover from the positive to the negative electrode.
3D geometry used in the simul
Field lines satisfying the streamer propagation condition (2) for discharges starting from
As demonstrated above, the method works well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in
introduce a truly three dimensional element, a block protruding from the inner high
conductor is added, see Fig. 13electric field is solved for and the particle tracing is carried out generating 1000 field lanalyze as is seen in Fig. post processing can be employed as for the 2D case shown earlier. As an example we display in
the field lines giving rise to a flashover from the positive to the negative electrode.
3D geometry used in the simul
Field lines satisfying the streamer propagation condition (2) for discharges starting from
As demonstrated above, the method works well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in
introduce a truly three dimensional element, a block protruding from the inner high
conductor is added, see Fig. 13electric field is solved for and the particle tracing is carried out generating 1000 field lanalyze as is seen in Fig. 14post processing can be employed as for the 2D
an example we display in the field lines giving rise to a flashover
from the positive to the negative electrode.
3D geometry used in the simul
Field lines satisfying the streamer propagation condition (2) for discharges starting from
As demonstrated above, the method works well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in
introduce a truly three dimensional element, a block protruding from the inner high
conductor is added, see Fig. 13electric field is solved for and the particle tracing is carried out generating 1000 field l
14. Exactly the same post processing can be employed as for the 2D
an example we display in the field lines giving rise to a flashover
from the positive to the negative electrode.
3D geometry used in the simul
Field lines satisfying the streamer propagation condition (2) for discharges starting from
As demonstrated above, the method works well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in
introduce a truly three dimensional element, a block protruding from the inner high
conductor is added, see Fig. 13electric field is solved for and the particle tracing is carried out generating 1000 field l
Exactly the same post processing can be employed as for the 2D
an example we display in the field lines giving rise to a flashover
from the positive to the negative electrode.
3D geometry used in the simul
Field lines satisfying the streamer propagation condition (2) for discharges starting from
As demonstrated above, the method works well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in
introduce a truly three dimensional element, a block protruding from the inner high
conductor is added, see Fig. 13electric field is solved for and the particle tracing is carried out generating 1000 field l
Exactly the same post processing can be employed as for the 2D
an example we display in the field lines giving rise to a flashover
from the positive to the negative electrode.
3D geometry used in the simul
Field lines satisfying the streamer propagation condition (2) for discharges starting from
As demonstrated above, the method works well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in
introduce a truly three dimensional element, a block protruding from the inner high
conductor is added, see Fig. 13electric field is solved for and the particle tracing is carried out generating 1000 field lines to
Exactly the same post processing can be employed as for the 2D
an example we display in the field lines giving rise to a flashover
from the positive to the negative electrode.
3D geometry used in the simulation.
Field lines satisfying the streamer propagation condition (2) for discharges starting from
As demonstrated above, the method works well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in
introduce a truly three dimensional element, a block protruding from the inner high
conductor is added, see Fig. 13. The electric field is solved for and the particle tracing
ines to Exactly the same
post processing can be employed as for the 2D an example we display in
the field lines giving rise to a flashover from the positive to the negative electrode.
ation.
Field lines satisfying the streamer propagation condition (2) for discharges starting from
As demonstrated above, the method works well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in
introduce a truly three dimensional element, a block protruding from the inner high
. The electric field is solved for and the particle tracing
ines to Exactly the same
post processing can be employed as for the 2D an example we display in
the field lines giving rise to a flashover
ation.
Field lines satisfying the streamer propagation condition (2) for discharges starting from
As demonstrated above, the method works well in 2D. Below we also show that it can easily be applied to 3D geometries as well. To illustrate this we rotate the 2D geometry used above to generate a corresponding 3D model. Then, in
introduce a truly three dimensional element, a block protruding from the inner high
. The electric field is solved for and the particle tracing
ines to Exactly the same
post processing can be employed as for the 2D an example we display in
the field lines giving rise to a flashover
propagation condition (2) for discharges starting from the positive electrode. Note the new flashover paths introduced from the protruding part of the 6. Conclusions
Module and in particular its ability toarbitrary quantities along field lines, it has become possible to evalucriteria in a relativelyengineering point of view this will have a significant impact on the design work on high voltage components, where the development of specialized inAs was demonstrated, the method works well in both
Figure
Figure
propagation condition (2) for discharges starting from the positive electrode. Note the new flashover paths introduced from the protruding part of the 6. Conclusions
With the introduction of the Particle Tracing Module and in particular its ability toarbitrary quantities along field lines, it has become possible to evalucriteria in a relativelyengineering point of view this will have a significant impact on the design work on high voltage components, where the development of specialized inAs was demonstrated, the method works well in both
Figure
Figure propagation condition (2) for discharges starting from the positive electrode.
Note the new flashover paths introduced from the protruding part of the
6. Conclusions
With the introduction of the Particle Tracing Module and in particular its ability toarbitrary quantities along field lines, it has become possible to evalucriteria in a relativelyengineering point of view this will have a significant impact on the design work on high voltage components, where the development of specialized inAs was demonstrated, the method works well in both 2D and 3D geometries.
Figure 1
Figure propagation condition (2) for discharges starting from the positive electrode.
Note the new flashover paths introduced from the protruding part of the
6. Conclusions
With the introduction of the Particle Tracing Module and in particular its ability toarbitrary quantities along field lines, it has become possible to evalucriteria in a relativelyengineering point of view this will have a significant impact on the design work on high voltage components, where the development of specialized inAs was demonstrated, the method works well in
2D and 3D geometries.
14. The 1000 field lines generated.
Figure 15. propagation condition (2) for discharges starting from the positive electrode.
Note the new flashover paths introduced from the protruding part of the
6. Conclusions
With the introduction of the Particle Tracing Module and in particular its ability toarbitrary quantities along field lines, it has become possible to evalucriteria in a relativelyengineering point of view this will have a significant impact on the design work on high voltage components, where the development of specialized in-As was demonstrated, the method works well in
2D and 3D geometries.
The 1000 field lines generated.
. Field lines satisfying the streamer propagation condition (2) for discharges starting from the positive electrode.
Note the new flashover paths introduced from the protruding part of the
6. Conclusions
With the introduction of the Particle Tracing Module and in particular its ability toarbitrary quantities along field lines, it has become possible to evalucriteria in a relativelyengineering point of view this will have a significant impact on the design work on high voltage components, where the development of
-house codes is no longer needed.As was demonstrated, the method works well in
2D and 3D geometries.
The 1000 field lines generated.
Field lines satisfying the streamer propagation condition (2) for discharges starting from the positive electrode.
Note the new flashover paths introduced from the protruding part of the
With the introduction of the Particle Tracing Module and in particular its ability toarbitrary quantities along field lines, it has become possible to evalucriteria in a relativelyengineering point of view this will have a significant impact on the design work on high voltage components, where the development of
house codes is no longer needed.As was demonstrated, the method works well in
2D and 3D geometries.
The 1000 field lines generated.
Field lines satisfying the streamer propagation condition (2) for discharges starting from
Note the new flashover paths introduced from the protruding part of the
With the introduction of the Particle Tracing Module and in particular its ability toarbitrary quantities along field lines, it has become possible to evalucriteria in a relatively simple manner. From an engineering point of view this will have a significant impact on the design work on high voltage components, where the development of
house codes is no longer needed.As was demonstrated, the method works well in
2D and 3D geometries.
The 1000 field lines generated.
Field lines satisfying the streamer propagation condition (2) for discharges starting from
Note the new flashover paths introduced from the protruding part of the high voltage electrode.
With the introduction of the Particle Tracing Module and in particular its ability toarbitrary quantities along field lines, it has become possible to evaluate streamer discharge
simple manner. From an engineering point of view this will have a significant impact on the design work on high voltage components, where the development of
house codes is no longer needed.As was demonstrated, the method works well in
2D and 3D geometries.
The 1000 field lines generated.
Field lines satisfying the streamer propagation condition (2) for discharges starting from
Note the new flashover paths introduced from high voltage electrode.
With the introduction of the Particle Tracing Module and in particular its ability toarbitrary quantities along field lines, it has
ate streamer discharge simple manner. From an
engineering point of view this will have a significant impact on the design work on high voltage components, where the development of
house codes is no longer needed.As was demonstrated, the method works well in
2D and 3D geometries.
The 1000 field lines generated.
Field lines satisfying the streamer propagation condition (2) for discharges starting from
Note the new flashover paths introduced from high voltage electrode.
With the introduction of the Particle Tracing Module and in particular its ability toarbitrary quantities along field lines, it has
ate streamer discharge simple manner. From an
engineering point of view this will have a significant impact on the design work on high voltage components, where the development of
house codes is no longer needed.As was demonstrated, the method works well in
The 1000 field lines generated.
Field lines satisfying the streamer propagation condition (2) for discharges starting from
Note the new flashover paths introduced from high voltage electrode.
With the introduction of the Particle Tracing Module and in particular its ability toarbitrary quantities along field lines, it has
ate streamer discharge simple manner. From an
engineering point of view this will have a significant impact on the design work on high voltage components, where the development of
house codes is no longer needed.As was demonstrated, the method works well in
The 1000 field lines generated.
Field lines satisfying the streamer propagation condition (2) for discharges starting from
Note the new flashover paths introduced from high voltage electrode.
With the introduction of the Particle Tracing Module and in particular its ability to integrate arbitrary quantities along field lines, it has
ate streamer discharge simple manner. From an
engineering point of view this will have a significant impact on the design work on high voltage components, where the development of
house codes is no longer needed.As was demonstrated, the method works well in
The 1000 field lines generated.
Field lines satisfying the streamer propagation condition (2) for discharges starting from
Note the new flashover paths introduced from high voltage electrode.
With the introduction of the Particle Tracing integrate
arbitrary quantities along field lines, it has ate streamer discharge
simple manner. From an engineering point of view this will have a significant impact on the design work on high voltage components, where the development of
house codes is no longer needed.As was demonstrated, the method works well in
Field lines satisfying the streamer propagation condition (2) for discharges starting from
Note the new flashover paths introduced from high voltage electrode.
With the introduction of the Particle Tracing integrate
arbitrary quantities along field lines, it has ate streamer discharge
simple manner. From an engineering point of view this will have a significant impact on the design work on high voltage components, where the development of
house codes is no longer needed.As was demonstrated, the method works well in
Field lines satisfying the streamer propagation condition (2) for discharges starting from
Note the new flashover paths introduced from
With the introduction of the Particle Tracing integrate
arbitrary quantities along field lines, it has ate streamer discharge
simple manner. From an engineering point of view this will have a significant impact on the design work on high voltage components, where the development of
house codes is no longer needed. As was demonstrated, the method works well in
7. References 1. Kuffel, E. and Zaengl, W.S., Engineering FundamentalsOxford (2.and Boehme, H., "Streamer inception and propagation models for power devices", Proc. CEIDP 2009 Conference, Virginia Beach (Oct. 2009)3. Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in Electrical Engineering, ETH Zurich4. breakdown criterion to inhomogeneous gas traps"
. References
1. Kuffel, E. and Zaengl, W.S., Engineering FundamentalsOxford (2. Pedersen, A., Christen, T., Blaszczyk, A., and Boehme, H., "Streamer inception and propagation models for power devices", Proc. CEIDP 2009 Conference, Virginia Beach (Oct. 2009)3. Christen, T., "Streamer Inception and Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in Electrical Engineering, ETH Zurich4. Petcharaks, K., "Applicability of the streamer breakdown criterion to inhomogeneous gas traps"
. References
1. Kuffel, E. and Zaengl, W.S., Engineering FundamentalsOxford (
Pedersen, A., Christen, T., Blaszczyk, A., and Boehme, H., "Streamer inception and propagation models for power devices", Proc. CEIDP 2009 Conference, Virginia Beach (Oct. 2009)
Christen, T., "Streamer Inception and Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in Electrical Engineering, ETH Zurich
Petcharaks, K., "Applicability of the streamer breakdown criterion to inhomogeneous gas traps", ETH Zurich Thesis No. 11192 (1995)
. References
1. Kuffel, E. and Zaengl, W.S., Engineering FundamentalsOxford (1984)
Pedersen, A., Christen, T., Blaszczyk, A., and Boehme, H., "Streamer inception and propagation models for power devices", Proc. CEIDP 2009 Conference, Virginia Beach (Oct. 2009)
Christen, T., "Streamer Inception and Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in Electrical Engineering, ETH Zurich
Petcharaks, K., "Applicability of the streamer breakdown criterion to inhomogeneous gas
ETH Zurich Thesis No. 11192 (1995)
. References
1. Kuffel, E. and Zaengl, W.S., Engineering Fundamentals
1984) Pedersen, A., Christen, T., Blaszczyk, A.,
and Boehme, H., "Streamer inception and propagation models for power devices", Proc. CEIDP 2009 Conference, Virginia Beach (Oct. 2009)
Christen, T., "Streamer Inception and Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in Electrical Engineering, ETH Zurich
Petcharaks, K., "Applicability of the streamer breakdown criterion to inhomogeneous gas
ETH Zurich Thesis No. 11192 (1995)
. References
1. Kuffel, E. and Zaengl, W.S., Engineering Fundamentals
Pedersen, A., Christen, T., Blaszczyk, A.,
and Boehme, H., "Streamer inception and propagation models for power devices", Proc. CEIDP 2009 Conference, Virginia Beach (Oct. 2009)
Christen, T., "Streamer Inception and Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in Electrical Engineering, ETH Zurich
Petcharaks, K., "Applicability of the streamer breakdown criterion to inhomogeneous gas
ETH Zurich Thesis No. 11192 (1995)
1. Kuffel, E. and Zaengl, W.S., Engineering Fundamentals
Pedersen, A., Christen, T., Blaszczyk, A., and Boehme, H., "Streamer inception and propagation models for power devices", Proc. CEIDP 2009 Conference, Virginia Beach (Oct. 2009)
Christen, T., "Streamer Inception and Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in Electrical Engineering, ETH Zurich
Petcharaks, K., "Applicability of the streamer breakdown criterion to inhomogeneous gas
ETH Zurich Thesis No. 11192 (1995)
1. Kuffel, E. and Zaengl, W.S., Engineering Fundamentals
Pedersen, A., Christen, T., Blaszczyk, A., and Boehme, H., "Streamer inception and propagation models for power devices", Proc. CEIDP 2009 Conference, Virginia Beach (Oct. 2009)
Christen, T., "Streamer Inception and Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in Electrical Engineering, ETH Zurich
Petcharaks, K., "Applicability of the streamer breakdown criterion to inhomogeneous gas
ETH Zurich Thesis No. 11192 (1995)
1. Kuffel, E. and Zaengl, W.S., Engineering Fundamentals
Pedersen, A., Christen, T., Blaszczyk, A., and Boehme, H., "Streamer inception and propagation models for designing air insulated power devices", Proc. CEIDP 2009 Conference, Virginia Beach (Oct. 2009)
Christen, T., "Streamer Inception and Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in Electrical Engineering, ETH Zurich
Petcharaks, K., "Applicability of the streamer breakdown criterion to inhomogeneous gas
ETH Zurich Thesis No. 11192 (1995)
1. Kuffel, E. and Zaengl, W.S., Engineering Fundamentals, Pergamon Press,
Pedersen, A., Christen, T., Blaszczyk, A., and Boehme, H., "Streamer inception and
designing air insulated power devices", Proc. CEIDP 2009 Conference,
Christen, T., "Streamer Inception and Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in Electrical Engineering, ETH Zurich
Petcharaks, K., "Applicability of the streamer breakdown criterion to inhomogeneous gas
ETH Zurich Thesis No. 11192 (1995)
1. Kuffel, E. and Zaengl, W.S., , Pergamon Press,
Pedersen, A., Christen, T., Blaszczyk, A., and Boehme, H., "Streamer inception and
designing air insulated power devices", Proc. CEIDP 2009 Conference,
Christen, T., "Streamer Inception and Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in Electrical Engineering, ETH Zurich
Petcharaks, K., "Applicability of the streamer breakdown criterion to inhomogeneous gas
ETH Zurich Thesis No. 11192 (1995)
1. Kuffel, E. and Zaengl, W.S., High, Pergamon Press,
Pedersen, A., Christen, T., Blaszczyk, A., and Boehme, H., "Streamer inception and
designing air insulated power devices", Proc. CEIDP 2009 Conference,
Christen, T., "Streamer Inception and Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in Electrical Engineering, ETH Zurich (Sep. 2012)
Petcharaks, K., "Applicability of the streamer breakdown criterion to inhomogeneous gas
ETH Zurich Thesis No. 11192 (1995)
High-Voltage , Pergamon Press,
Pedersen, A., Christen, T., Blaszczyk, A., and Boehme, H., "Streamer inception and
designing air insulated power devices", Proc. CEIDP 2009 Conference,
Christen, T., "Streamer Inception and Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in
(Sep. 2012)Petcharaks, K., "Applicability of the streamer
breakdown criterion to inhomogeneous gas ETH Zurich Thesis No. 11192 (1995)
Voltage , Pergamon Press,
Pedersen, A., Christen, T., Blaszczyk, A., and Boehme, H., "Streamer inception and
designing air insulated power devices", Proc. CEIDP 2009 Conference,
Christen, T., "Streamer Inception and Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in
(Sep. 2012)Petcharaks, K., "Applicability of the streamer
breakdown criterion to inhomogeneous gas ETH Zurich Thesis No. 11192 (1995)
Voltage , Pergamon Press,
Pedersen, A., Christen, T., Blaszczyk, A., and Boehme, H., "Streamer inception and
designing air insulated power devices", Proc. CEIDP 2009 Conference,
Christen, T., "Streamer Inception and Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in
(Sep. 2012) Petcharaks, K., "Applicability of the streamer
breakdown criterion to inhomogeneous gas
Voltage , Pergamon Press,
Pedersen, A., Christen, T., Blaszczyk, A., and Boehme, H., "Streamer inception and
designing air insulated power devices", Proc. CEIDP 2009 Conference,
Christen, T., "Streamer Inception and Propagation from Electric Field Simulations", Proc. SCEE2012 Scientific Computing in
Petcharaks, K., "Applicability of the streamer
breakdown criterion to inhomogeneous gas