today’s outline - january 28, 2020phys.iit.edu/~segre/phys570/20s/lecture_05.pdf · today’s...

Today’s outline - January 28, 2020

• Undulator harmonics

• Undulator coherence

• Emittance

• Time structure

• APS-U, ERLs and FELs• Detectors

• Gas detectors• Scintillation counters• Solid state detectors• Area detectors

Reading Assignment: Chapter 3.1–3.3

Homework Assignment #01:Chapter 2: 2,3,5,6,8due Thursday, January 30, 2020

C. Segre (IIT) PHYS 570 - Spring 2020 January 28, 2020 1 / 33

• Emittance

• Time structure

• Emittance

• Time structure

• Emittance

• Time structure

• Emittance

• Time structure

• Emittance

• Time structure

• APS-U, ERLs and FELs

• Detectors

• Emittance

• Time structure

• Emittance

• Time structure

• Gas detectors

• Scintillation counters• Solid state detectors• Area detectors

• Emittance

• Time structure

• Gas detectors• Scintillation counters

• Solid state detectors• Area detectors

• Emittance

• Time structure

• Gas detectors• Scintillation counters• Solid state detectors

• Area detectors

• Emittance

• Time structure

• Emittance

• Time structure

• Emittance

• Time structure

Undulator review

For an undulator of period λu we have derived the following undulatorparameters and their relationships:

the K parameter, a dimension-less quantity which represents the“strength” of the undulator

the electron path length throughthe undulator, Sλu

the fundamental wavelength of theundulator, λ1 and the origin of theodd and even harmonics

2πmcλuB0

= 0.934λu[cm]B0[T]

Sλu ≈ λu(

λ1 ≈λu2γ2

)Now let us look at the coherence of the undulator radiation

Undulator review

2πmcλuB0

= 0.934λu[cm]B0[T]

Sλu ≈ λu(

λ1 ≈λu2γ2

Undulator review

2πmcλuB0

= 0.934λu[cm]B0[T]

Sλu ≈ λu(

λ1 ≈λu2γ2

Undulator review

2πmcλuB0

= 0.934λu[cm]B0[T]

Sλu ≈ λu(

λ1 ≈λu2γ2

Undulator review

2πmcλuB0

= 0.934λu[cm]B0[T]

Sλu ≈ λu(

λ1 ≈λu2γ2

Undulator review

2πmcλuB0

= 0.934λu[cm]B0[T]

Sλu ≈ λu(

λ1 ≈λu2γ2

Undulator review

the fundamental wavelength of theundulator, λ1

and the origin of theodd and even harmonics

2πmcλuB0

= 0.934λu[cm]B0[T]

Sλu ≈ λu(

λ1 ≈λu2γ2

Undulator review

the fundamental wavelength of theundulator, λ1

and the origin of theodd and even harmonics

2πmcλuB0

= 0.934λu[cm]B0[T]

Sλu ≈ λu(

λ1 ≈λu2γ2

Now let us look at the coherence of the undulator radiation

Undulator review

2πmcλuB0

= 0.934λu[cm]B0[T]

Sλu ≈ λu(

λ1 ≈λu2γ2

Now let us look at the coherence of the undulator radiation

Undulator review

2πmcλuB0

= 0.934λu[cm]B0[T]

Sλu ≈ λu(

λ1 ≈λu2γ2

Diffraction grating

An N period undulator is basically like a diffraction grating, only in thetime domain rather than the space domain.

A diffraction grating consists of N coherent sources whose emission isdetected at a single point.

The radiation from each slit has totravel a slightly different distance toget to the detector. For consecu-tive slits this path length difference,Lm+1 − Lm = δL, gives rise to aphase shift, 2πε = 2πδL/λ. So at thedetector, we have a sum of waves:

N−1∑m=0

e i(~k·~r+2πmε) = e i

~k·~rN−1∑m=0

e i2πmε

the phase shift from each undulatorpole depends on the wavelength λu

Diffraction grating

An N period undulator is basically like a diffraction grating, only in thetime domain rather than the space domain.A diffraction grating consists of N coherent sources whose emission isdetected at a single point.

N−1∑m=0

~k·~rN−1∑m=0

e i2πmε

Diffraction grating

The radiation from each slit has totravel a slightly different distance toget to the detector.

For consecu-tive slits this path length difference,Lm+1 − Lm = δL, gives rise to aphase shift, 2πε = 2πδL/λ. So at thedetector, we have a sum of waves:

N−1∑m=0

~k·~rN−1∑m=0

e i2πmε

Diffraction grating

The radiation from each slit has totravel a slightly different distance toget to the detector. For consecu-tive slits this path length difference,Lm+1 − Lm = δL,

gives rise to aphase shift, 2πε = 2πδL/λ. So at thedetector, we have a sum of waves:

N−1∑m=0

~k·~rN−1∑m=0

e i2πmε

Diffraction grating

The radiation from each slit has totravel a slightly different distance toget to the detector. For consecu-tive slits this path length difference,Lm+1 − Lm = δL, gives rise to aphase shift, 2πε = 2πδL/λ.

So at thedetector, we have a sum of waves:

N−1∑m=0

~k·~rN−1∑m=0

e i2πmε

Diffraction grating

N−1∑m=0

e i(~k·~r+2πmε)

= e i~k·~r

N−1∑m=0

e i2πmε

Diffraction grating

N−1∑m=0

~k·~rN−1∑m=0

e i2πmε

Diffraction grating

N−1∑m=0

~k·~rN−1∑m=0

e i2πmε

Geometric series

The sum is simply a geometric series, SN with k = e i2πε

SN =N−1∑m=0

km = 1 + k + k2 + · · ·+ kN−2 + kN−1

We can develop a recursion relation by writing the expression for SN−1

SN−1 =N−2∑m=0

km = 1 + k + k2 + · · ·+ kN−2

so we can write that SN−1 = SN − kN−1 and

SN = 1 + kSN−1 = 1 + k(SN − kN−1) = 1 + kSN − kN

Solving for SN , we have

SN − kSN = 1− kN −→ SN =1− kN

1− k

Geometric series

SN =N−1∑m=0

= 1 + k + k2 + · · ·+ kN−2 + kN−1

SN−1 =N−2∑m=0

km = 1 + k + k2 + · · ·+ kN−2

SN − kSN = 1− kN −→ SN =1− kN

1− k

Geometric series

SN =N−1∑m=0

km = 1 + k + k2 + · · ·+ kN−2 + kN−1

SN−1 =N−2∑m=0

km = 1 + k + k2 + · · ·+ kN−2

SN − kSN = 1− kN −→ SN =1− kN

1− k

Geometric series

SN =N−1∑m=0

km = 1 + k + k2 + · · ·+ kN−2 + kN−1

SN−1 =N−2∑m=0

km = 1 + k + k2 + · · ·+ kN−2

SN − kSN = 1− kN −→ SN =1− kN

1− k

Geometric series

SN =N−1∑m=0

km = 1 + k + k2 + · · ·+ kN−2 + kN−1

SN−1 =N−2∑m=0

km = 1 + k + k2 + · · ·+ kN−2

so we can write that SN−1 = SN − kN−1

SN − kSN = 1− kN −→ SN =1− kN

1− k

Geometric series

SN =N−1∑m=0

km = 1 + k + k2 + · · ·+ kN−2 + kN−1

SN−1 =N−2∑m=0

km = 1 + k + k2 + · · ·+ kN−2

SN = 1 + kSN−1

= 1 + k(SN − kN−1) = 1 + kSN − kN

SN − kSN = 1− kN −→ SN =1− kN

1− k

Geometric series

SN =N−1∑m=0

km = 1 + k + k2 + · · ·+ kN−2 + kN−1

SN−1 =N−2∑m=0

km = 1 + k + k2 + · · ·+ kN−2

SN = 1 + kSN−1 = 1 + k(SN − kN−1)

= 1 + kSN − kN

SN − kSN = 1− kN −→ SN =1− kN

1− k

Geometric series

SN =N−1∑m=0

km = 1 + k + k2 + · · ·+ kN−2 + kN−1

SN−1 =N−2∑m=0

km = 1 + k + k2 + · · ·+ kN−2

SN − kSN = 1− kN −→ SN =1− kN

1− k

Geometric series

SN =N−1∑m=0

km = 1 + k + k2 + · · ·+ kN−2 + kN−1

SN−1 =N−2∑m=0

km = 1 + k + k2 + · · ·+ kN−2

SN − kSN = 1− kN −→ SN =1− kN

1− k

Geometric series

SN =N−1∑m=0

km = 1 + k + k2 + · · ·+ kN−2 + kN−1

SN−1 =N−2∑m=0

km = 1 + k + k2 + · · ·+ kN−2

SN − kSN = 1− kN

−→ SN =1− kN

1− k

Geometric series

SN =N−1∑m=0

km = 1 + k + k2 + · · ·+ kN−2 + kN−1

SN−1 =N−2∑m=0

km = 1 + k + k2 + · · ·+ kN−2

SN − kSN = 1− kN −→ SN =1− kN

1− k

Intensity from a diffraction grating

Restoring the expression for k = e i2πε, we have:

N−1∑m=0

e i2πmε = SN =1− e i2πNε

1− e i2πε=

(e−iπNε − e iπNε

e−iπε − e iπε

)e iπNε

e iπε

(sin (πNε)

sin (πε)

)e iπ(N−1)ε

Therefore, for the diffraction grating we can calculate the intensity at thedetector as

∣∣∣∣∣e i~k·~rN−1∑m=0

e i2πmε

∣∣∣∣∣2

=∣∣∣e i~k·~rSN

∣∣∣2 =

∣∣∣∣e i~k·~r sin (πNε)

sin (πε)e iπ(N−1)ε

∣∣∣∣2

I =sin2 (πNε)

sin2 (πε)

N−1∑m=0

e i2πmε = SN

=1− e i2πNε

1− e i2πε=

)e iπNε

e iπε

(sin (πNε)

sin (πε)

)e iπ(N−1)ε

∣∣∣∣∣e i~k·~rN−1∑m=0

e i2πmε

∣∣∣∣∣2

∣∣∣2 =

∣∣∣∣2

I =sin2 (πNε)

sin2 (πε)

N−1∑m=0

1− e i2πε

)e iπNε

e iπε

(sin (πNε)

sin (πε)

)e iπ(N−1)ε

∣∣∣∣∣e i~k·~rN−1∑m=0

e i2πmε

∣∣∣∣∣2

∣∣∣2 =

∣∣∣∣2

I =sin2 (πNε)

sin2 (πε)

N−1∑m=0

1− e i2πε=

)e iπNε

e iπε

(sin (πNε)

sin (πε)

)e iπ(N−1)ε

∣∣∣∣∣e i~k·~rN−1∑m=0

e i2πmε

∣∣∣∣∣2

∣∣∣2 =

∣∣∣∣2

I =sin2 (πNε)

sin2 (πε)

N−1∑m=0

1− e i2πε=

)e iπNε

e iπε

(sin (πNε)

sin (πε)

)e iπ(N−1)ε

∣∣∣∣∣e i~k·~rN−1∑m=0

e i2πmε

∣∣∣∣∣2

∣∣∣2 =

∣∣∣∣2

I =sin2 (πNε)

sin2 (πε)

N−1∑m=0

1− e i2πε=

)e iπNε

e iπε

(sin (πNε)

sin (πε)

)e iπ(N−1)ε

∣∣∣∣∣e i~k·~rN−1∑m=0

e i2πmε

∣∣∣∣∣2

∣∣∣2 =

∣∣∣∣2

I =sin2 (πNε)

sin2 (πε)

N−1∑m=0

1− e i2πε=

)e iπNε

e iπε

(sin (πNε)

sin (πε)

)e iπ(N−1)ε

∣∣∣∣∣e i~k·~rN−1∑m=0

e i2πmε

∣∣∣∣∣2

∣∣∣2 =

∣∣∣∣2

I =sin2 (πNε)

sin2 (πε)

N−1∑m=0

1− e i2πε=

)e iπNε

e iπε

(sin (πNε)

sin (πε)

)e iπ(N−1)ε

∣∣∣∣∣e i~k·~rN−1∑m=0

e i2πmε

∣∣∣∣∣2

∣∣∣2

∣∣∣∣2

I =sin2 (πNε)

sin2 (πε)

N−1∑m=0

1− e i2πε=

)e iπNε

e iπε

(sin (πNε)

sin (πε)

)e iπ(N−1)ε

∣∣∣∣∣e i~k·~rN−1∑m=0

e i2πmε

∣∣∣∣∣2

∣∣∣2 =

∣∣∣∣2

I =sin2 (πNε)

sin2 (πε)

N−1∑m=0

1− e i2πε=

)e iπNε

e iπε

(sin (πNε)

sin (πε)

)e iπ(N−1)ε

∣∣∣∣∣e i~k·~rN−1∑m=0

e i2πmε

∣∣∣∣∣2

∣∣∣2 =

∣∣∣∣2

I =sin2 (πNε)

sin2 (πε)

Beam coherence

2πε=0

0 10 20 30 40

2πε [degrees]

nsity (

units)

With the height and width of the peak dependent on the number of poles.

Beam coherence

2πε=0

0 10 20 30 40

2πε [degrees]

nsity (

Beam coherence

2πε=5o

0 10 20 30 40

2πε [degrees]

nsity (

Beam coherence

2πε=10o

0 10 20 30 40

2πε [degrees]

nsity (

Beam coherence

2πε=15o

0 10 20 30 40

2πε [degrees]

nsity (

Beam coherence

2πε=20o

0 10 20 30 40

2πε [degrees]

nsity (

Beam coherence

2πε=25o

0 10 20 30 40

2πε [degrees]

nsity (

Beam coherence

2πε=30o

0 10 20 30 40

2πε [degrees]

nsity (

Beam coherence

2πε=35o

0 10 20 30 40

2πε [degrees]

nsity (

Beam coherence

2πε=40o

0 10 20 30 40

2πε [degrees]

nsity (

Beam coherence

2πε=45o

0 10 20 30 40

2πε [degrees]

nsity (

Beam coherence

2πε=45o

0 10 20 30 40

2πε [degrees]

nsity (

Undulator monochromaticity

nsity (

32 poles

16 poles

96 poles

The more poles in the undulator,the more monochromatic the beamsince a slight change in ε = δL/λimplies a slightly different wave-length λ

Another way to look at this is thatthe longer the undulator, the longerthe pulse train in time and the nar-rower the frequency distribution inits Fourier Transform

The APS has a 72 pole undulatorof 3.3 cm period

Higher order harmonics have nar-rower energy bandwidth but lowerpeak intensity

nsity (

32 poles

16 poles

96 poles

nsity (

32 poles

16 poles

96 poles

nsity (

harmonic

1st harmonic

Synchrotron time structure

There are two importanttime scales for a storagering such as the APS: pulselength and interpulse spacing

The APS pulse length in 24-bunch mode is 90 ps whilethe pulses come every 154 ns

Other modes include single-bunch mode for timing ex-periments and 324-bunchmode (inter pulse timing of11.7 ns) for a more constantx-ray flux

Emittance

Is there a limit to the brilliance of an undulator source at a synchrotron?

the brilliance is inversely proportional to the square of the product of thelinear source size and the angular divergence

brilliance =flux [photons/s]

divergence[mrad2

]· source size [mm2] [0.1% bandwidth]

the product of the source size and divergence iscalled the emittance, ε and the brilliance is thuslimited by the product of the emittance of theradiation in the horizontal and vertical directionsεxεy

this emittance cannot be changed but it can berotated or deformed by magnetic fields as theelectron beam travels around the storage ringas long as the area is kept constant

Emittance

divergence[mrad2

Emittance

divergence[mrad2

the product of the source size and divergence iscalled the emittance, ε

and the brilliance is thuslimited by the product of the emittance of theradiation in the horizontal and vertical directionsεxεy

Emittance

divergence[mrad2

Emittance

divergence[mrad2

this emittance cannot be changed but it can berotated

or deformed by magnetic fields as theelectron beam travels around the storage ringas long as the area is kept constant

Emittance

divergence[mrad2

APS emittance

For photon emission from a single electron in a 2m undulator at 1A

10µrad

-10µrad

10µm-10µm

σradiation = 9.1µm

σ′radiation = 7.7µrad

√Lλ

4π= 1.3µm

σ′γ=

L= 7.1µrad

current APS electron beamparameters are

σy= 9.1µm

σ′y= 3.0µrad

must convolute to get pho-ton emission from entirebeam (in vertical direction)

APS emittance

10µrad

-10µrad

10µm-10µm

√Lλ

4π= 1.3µm

σ′γ=

L= 7.1µrad

σy= 9.1µm

σ′y= 3.0µrad

APS emittance

10µrad

-10µrad

10µm-10µm

√Lλ

4π= 1.3µm

σ′γ=

L= 7.1µrad

σy= 9.1µm

σ′y= 3.0µrad

APS emittance

10µrad

-10µrad

10µm-10µm

√Lλ

4π= 1.3µm

σ′γ=

L= 7.1µrad

σy= 9.1µm

σ′y= 3.0µrad

APS emittance

10µrad

-10µrad

10µm-10µm

√Lλ

4π= 1.3µm

σ′γ=

L= 7.1µrad

σy= 9.1µm

σ′y= 3.0µrad

APS emittance

10µrad

-10µrad

10µm-10µm

√Lλ

4π= 1.3µm

σ′γ=

L= 7.1µrad

σy= 9.1µm

σ′y= 3.0µrad

APS emittance

10µrad

-10µrad

10µm-10µm

√Lλ

4π= 1.3µm

σ′γ=

L= 7.1µrad

σy= 9.1µm

σ′y= 3.0µrad

APS emittance

10µrad

-10µrad

10µm-10µm

√Lλ

4π= 1.3µm

σ′γ=

L= 7.1µrad

σy= 9.1µm

σ′y= 3.0µrad

Evolution of APS parameters

Parameter 1995 2001 2005σx 334 µm 352 µm 280 µmσ′x 24 µrad 22 µrad 11.6 µrad

σy 89 µm 18.4 µm 9.1 µmσ′y 8.9 µrad 4.2 µrad 3.0 µrad

When first commissioned in 1995, the APS electron beam size anddivergence was relatively large, particularly in the horizontal, x direction

By the end of the first decade of operation, the horizontal source sizedecreased by about 16% and its horizontal divergence by more than 50%

At the same time the vertical source size decreased by over 90% and thevertical divergence by nearly 67%

The next big upgrade (slated for 2022) will make the beam more square inspace and by choosing the undulator correctly, a higher performanceinsertion device.

APS upgrade

In 2022, the APS will shut down for a major rebuild with a totally newmagnetic lattice.

One of the biggest changes will be the beam (source)size and emittance

Position (µm)

Positio

6003000-300-600

Position (µm)

Positio

6003000-300-600

The beam will be nearly square and there will be much more coherencefrom the undulators

APS upgrade

In 2022, the APS will shut down for a major rebuild with a totally newmagnetic lattice. One of the biggest changes will be the beam (source)size and emittance

Position (µm)

Positio

6003000-300-600

Position (µm)

Positio

6003000-300-600

APS upgrade

Position (µm)

Positio

6003000-300-600

Position (µm)

Positio

6003000-300-600

APS upgrade

Position (µm)

Positio

6003000-300-600

Position (µm)

Positio

6003000-300-600

APS upgrade

Position (µm)

Positio

6003000-300-600

Position (µm)

Positio

6003000-300-600

APSU undulator performance

The APS upgrade will bea diffraction-limited sourcewith a lower energy (6.0GeV) and doubled current(200 mA).

Since MRCAT’s science isprimarily flux driven, the goalwill be to replace the 2.4mundulator with one that out-performs the current 33mmperiod but with only modestincrease in power.

The APS is calling this a“4th” generation synchrotronsource

0 10 20 30 40Photon Energy (keV)

Density (

APS 33 mm

Density (

APS 33 mm

Energy recovery linacs

Undulators have limited peak brilliance

but the use of an energy recoverylinac can overcome this limitation and enhance peak brilliance by up tothree orders of magnitude

Undulators have limited peak brilliance but the use of an energy recoverylinac can overcome this limitation and enhance peak brilliance by up tothree orders of magnitude

Free electron laser

Initial electron cloud, each electron emits co-herently but independently

Over course of 100 m, electric field of pho-tons, feeds back on the electron bunch

Microbunches form with period of FEL (andradiation in electron frame)

Each microbunch emits coherently withneighboring ones

Again, an alternative way to view this is that the pulse train from a 100mlong undulator is long enough in time to produce a monochromatic andcoherent frequency distribution when Fourier Transformed

Free electron laser

FEL emission

FEL layout

An FEL has a single accelerator whose electron beam is shuntedsequentially through different undulators and end stations

The single pass of the electron beam permits a very low emittance to beachieved and thus higher coherence

The high brightness usually results in destruction of the sample during theillumination, thus the need for multiple samples and multiple shotexperiments

FEL layout

Compact sources

Lyncean CLS

Types of X-ray Detectors

Gas detectors

• Ionization chamber

• Proportional counter

• Geiger-Muller tube

Scintillation countersSolid state detectors

• Intrinsic semiconductor

• P-I-N junction

• Silicon drift

Charge coupled device detectors

• Indirect

• Direct coupled

Gas detectors

• P-I-N junction

• Silicon drift

• Indirect

• Direct coupled

Gas detectors

Scintillation counters

Solid state detectors

• P-I-N junction

• Silicon drift

• Indirect

• Direct coupled

Gas detectors

• P-I-N junction

• Silicon drift

• Indirect

• Direct coupled

Gas detectors

• P-I-N junction

• Silicon drift

• Indirect

• Direct coupled

Gas detectors

• P-I-N junction

• Silicon drift

• Indirect

• Direct coupled

Gas detectors

• P-I-N junction

• Silicon drift

• Indirect

• Direct coupled

Gas detectors

• P-I-N junction

• Silicon drift

• Indirect

• Direct coupled

Gas detectors

• P-I-N junction

• Silicon drift

• Indirect

• Direct coupled

Gas detectors

• P-I-N junction

• Silicon drift

• Indirect

• Direct coupled

Gas detectors

• P-I-N junction

• Silicon drift

• Indirect

• Direct coupled

Gas detectors

• P-I-N junction

• Silicon drift

• Indirect

• Direct coupled

Gas detectors

• P-I-N junction

• Silicon drift

• Indirect

• Direct coupled

Gas Detectors

Gas detectors operate in several modes depending on the particle type, gascomposition and pressure and voltage applied

The most interesting arethe ionization, propor-tional, and Geiger-Muller

At a synchrotron, the par-ticle being detected ismost often a photon (γ)

The most useful regimeis the ionization regionwhere the output pulseis independent of the ap-plied voltage over a widerange

Applied Voltage

ation C

ited P

roport

Muelle

Continuous D

ischarg

Gas Detectors

Applied Voltage

ation C

ited P

roport

Muelle

Continuous D

ischarg

Gas Detectors

Applied Voltage

ation C

ited P

roport

Muelle

Continuous D

ischarg

Gas Detectors

Applied Voltage

ation C

ited P

roport

Muelle

Continuous D

ischarg

Ionization Chamber

Useful for beam monitoring, flux measurement, fluorescence measurement,spectroscopy.

window

x-rays

current collector A

• Closed (or sealed) chamber oflength L with gas mixtureµ =

∑ρiµi

• High voltage applied to plates

• Calculate fraction of beamabsorbed I/I0 = e−µL

• When x-ray interacts with gasatom, photoionized electronsswept rapidly to positiveelectrode and current (nanoAmperes) is measured.

• Count rates up to 1011

photons/s/cm3

• 22-41 eV per electron-ion pair(depending on the gas) makesthis useful for quantitativemeasurements.

Ionization Chamber

window

x-rays

current collector A

∑ρiµi

photons/s/cm3

Ionization Chamber

window

x-rays

current collector A

∑ρiµi

photons/s/cm3

Ionization Chamber

window

x-rays

current collector A

∑ρiµi

photons/s/cm3

Ionization Chamber

window

x-rays

current collector A

∑ρiµi

photons/s/cm3

Ionization Chamber

window

x-rays

current collector A

∑ρiµi

photons/s/cm3

Ionization Chamber

window

x-rays

current collector A

∑ρiµi

photons/s/cm3

Getting a reading

The ionization chamber puts out a current in the nA range, this needs tobe converted into a useful measurement

Ionization

Chamber

Voltage to

Frequency

Transconductance

Amplifier

[nA] [kHz]Scaler

the tiny current is fed into an sensitive amplifier with gains of up to 1010

which outputs a voltage signal of 1-10 V that tracks the input with anadjustable time constant

the voltage is converted to a digital signal by a Voltage to Frequencyconverter which outputs 100 kHz (or more) pulse frequency per Volt ofinput

the digital pulse train is counted by a scaler for a user-definable length oftime

Getting a reading

Ionization

Chamber

[V] Voltage to

Frequency

Transconductance

Amplifier

[nA] [kHz]Scaler

Getting a reading

Ionization

Chamber

[V] Voltage to

Frequency

Transconductance

Amplifier

[nA] [kHz]Scaler

Getting a reading

Ionization

Chamber

[V] Voltage to

Frequency

Transconductance

Amplifier

[nA] [kHz]Scaler

Scintillation detector

Useful for photon counting experiments with rates less than 104/s

• NaI(Tl), Yttrium Aluminum Perovskite (YAP) or plastic which,absorb x-rays and fluoresce in the visible spectrum.• Light strikes a thin photocathode which emits electrons into the

vacuum portion of a photomultiplier tube.• Photoelectrons are accelerated in steps, striking dynodes and

becoming amplified.• Output voltage pulse is proportional to initial x-ray energy.

• NaI(Tl), Yttrium Aluminum Perovskite (YAP) or plastic which,absorb x-rays and fluoresce in the visible spectrum.

• Light strikes a thin photocathode which emits electrons into thevacuum portion of a photomultiplier tube.• Photoelectrons are accelerated in steps, striking dynodes and

vacuum portion of a photomultiplier tube.

• Photoelectrons are accelerated in steps, striking dynodes andbecoming amplified.• Output voltage pulse is proportional to initial x-ray energy.

becoming amplified.

• Output voltage pulse is proportional to initial x-ray energy.

Counting a scintillator pulse

the scintillator and photomultiplier put out avery fast negative-going tail pulse which is por-portional to the energy of the photon

a fast shaping and inverting amplifier is used toconvert this fast tail pulse to a more completepositive voltage pulse which can be processed

an energy discriminator with a threshold, E , andwindow ∆E is used to detect if the voltage pulsehas the desired height (which corresponds to thex-ray energy to be detected)

if the voltage pulse falls within the discriminatorwindow, a short digital pulse is output from thediscriminator and into a scaler for counting

The energy resolution of a scintillator is very poor and it is often necessaryto be able to distinguish the energy of specific x-rays. The semiconductordetector is ideal for this purpose.

a semiconductor such as Si or Ge has a com-pletely filled valence band and an empty con-duction band separated by an energy gap ∆Eof ∼ 1.2 eV for Si and ∼ 0.7 eV for Ge

when a photon is absorbed by the semicon-ductor, it promotes electrons from the va-lence to the conduction band creating anelectron-hole pair

Valence Band

Conduction Band

because of the small energy required to produce an electron-hole pair, onex-ray photon will create many and its energy can be detected with veryhigh resolution

Valence Band

Conduction Band

Valence Band

Conduction Band

Valence Band

Conduction Band

Semiconductor junctions

Producing the electron-hole pairs is not sufficient. It is necessary toextract the charge from the device to make a measurement

start with two pieces of semiconductor,one n-type and the other p-type

if these two materials are brought intocontact, a natural depletion region isformed where there is an electric field ~E

depletion region

this region is called an intrinsic region and is the only place where anabsorbed photon can create electron-hole pairs and have them be swept tothe p and n sides, respectively

by applying a reverse bias voltage, it is possible to extend the depletedregion, make the effective volume of the detector larger and increase theelectric field to get faster charge collection times

depletion region

Silicon Drift Detector

Same principle as intrinsic or p-i-n detector but much more compact andoperates at higher temperatures

Relatively low stopping power is a drawback

Detector operation

Li metal

P-doped+Vbias

A A A A1 2 3 4pile up

output current is integrated into voltage pulses by a pre-amp, whenmaximum voltage is reached, output is optically reset

fast channel “sees” steps and starts integration; pulse heights are measuredwith slow channel by integration; and detected pulse pileups are rejected

electronics outputs input count rate (icr), output count rate (ocr), andareas of integrated pulses (An)

Detector operation

Li metal

P-doped+Vbias

Detector operation

Li metal

P-doped+Vbias

fast channel “sees” steps and starts integration;

pulse heights are measuredwith slow channel by integration; and detected pulse pileups are rejected

Detector operation

Li metal

P-doped+Vbias

Detector operation

Li metal

P-doped+Vbias

Dead time correction

Input Count Rate (kcps)

0 50 100 150 2000

actual ocr

ideal ocr

the output count rateis significantly lowerthan the input countrate and gets worsewith higher photonrate

if these curves areknown, a dead timecorrection can be ap-plied to correct for roll-off

if dead time is toolarge, correction willnot be accurate!

0 50 100 150 2000

actual ocr

ideal ocr

0 50 100 150 2000

actual ocr

ideal ocr

0 50 100 150 2000

actual ocr

ideal ocr

SDD spectrum

0 5000 10000 15000

Energy (eV)

Counts

fluorescence spectrumof Cu foil in air using9200 eV x-rays

Compton peak is visi-ble just above the CuKα fluorescence line

Ar fluorescence near3000 eV

a small amount ofpulse pileup is visiblenear 16000 eV

SDD spectrum

0 5000 10000 15000

Energy (eV)

Counts

SDD spectrum

0 5000 10000 15000

Energy (eV)

Counts

SDD spectrum

0 5000 10000 15000

Energy (eV)

Counts

SDD spectrum

0 5000 10000 15000

Energy (eV)

Counts

today’s outline - january 28, 2020phys.iit.edu/~segre/phys570/20s/lecture_05.pdf · today’s...

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