statistical analysis of locked modes and their...

1

Disruptive LMs/QSMs with TM precursors

0 20 40 60 80 100Time (ms) after n=1 LM/QSM appearance

6

8

10

12

14

16

18

20

B r (G

) of L

M/Q

SM0.5

1.0

1.5

2.0

2.5

log 1

0N

By

R. Sweeney*, W. Choi*, K.E.J. Olofsson, F. Volpe Columbia University Presented at the

56th Annual Meeting of the American Physical Society Division of Plasma Physics October 27-31, 2014 New Orleans, LA

Statistical Analysis of Locked Modes and Their Disruptivity at DIII-D

R. Sweeney, W. Choi/APS-DPP/October 2014

*Authors contributed equally

2

A database has been developed to study locking and disruptivity

of neoclassical tearing modes (NTMs) with poloidal and toroidal

mode numbers m=2 and n=1. Approximately 18,500 DIII-D

discharges are studied providing statistics on the fraction of

disruptions containing locked modes (LMs) and the ratio of

disruptive LMs to all LMs. Other quantities analyzed include the

time-scales between mode-formation and locking, and between

locking and disruption, the amplitude of the mode upon locking

and disruption, and the existence or lack of a rotating precursor.

Simple interpretations are provided in terms of island size and

torques acting on the island, and implications for an automatic

locked mode controller are discussed.

Abstract


3

Motivation

•  2/1 locked mode (LM) predicted to be disruptive in ITER1

•  Control techniques would benefit from statistical knowledge of

relevant time-scales, typical mode amplitudes and other

physical quantities to be controlled2

•  Database makes possible the study of correlations between

LM/QSM properties and plasma properties

•  Provides useful knowledge to better understand LM physics

1Buttery, PoP 2008 2Volpe, PoP 2009 R. Sweeney, W. Choi/APS-DPP/October 2014

4

Two distinct mode evolutions are considered in this database


6200 6250 6300 6350 6400 6450 6500Time (ms)

05

1015202530

B r (G

) of m

=eve

n, n

=1 N

TM

051015202530

B r (G

) of n

=1 Q

SM o

r LM

159429

2000 2100 2200 2300 2400Time (ms)

0102030405060

B r (G

) of m

=eve

n, n

=1 N

TM

0

5

10

15

20

25

B r (G

) of n

=1 Q

SM o

r LM

159424 f×4 (kHz)

θ θ

5

Automatic analysis of rotating NTMs and LMs/QSMs designed to be simple and robust

•  n=1, m=even rotating NTM detection -  Cross-power and cross-phase between two magnetic probes

identifies rotating n=1 signal (newspec code) -  Mode shape identification differentiates m=even/odd (eigspec

code) -  Thresholding and requirements on signal/noise ratio determines

whether NTM exists

•  n=1 LM or QSM detection –  Least-squares fit of pair-differenced, coil-compensated external

saddle loops (ESLDs) provides n=1 amplitude and phase (assumes n ≥ 5 mode amplitudes negligible)

–  Automatic background subtraction removes integrator drift and other undesired sources of Br

–  LM or QSM must be > 5 G for detection •  Mode termination defined by Br passing below 1.25 G


6

Eigspec: a magnetic probe array analysis algorithm for NTMs via Stochastic Subspace Identification (SSI)1


1800 1850 1900 1950 2000 20500

0.5

1

1.5

2

2.5

3

3.5

t [ms]

RM

S (b

) [m

T]

n=−1 (+)n=−1 (−)nolabel

•  Given Mirnov probe array data –  Extracts common

frequencies via SSI –  Finds spatial features

matching the frequencies –  Returns mode amplitude,

frequency, and mode type

•  Using 10 probes –  9 on out-board mid-plane –  1 on in-board mid-plane

•  Able to identify –  n number –  m = even or odd

Example output for simplified eigspec: shot 159424, red trace shows m=even, n=1 mode growing

(even) (odd)

1Olofsson, PPCF 2014

7

Physically informed automatic piecewise-linear background subtraction of ESLDs improves detection

•  Integrator drift and changes in the plasma equilibrium can cause spurious n=1 signals in the ESLDs

•  These background signals are greatly reduced by removing a piecewise-linear function, effectively “zeroing” the n=1 signal at the following times: -  100 ms before and after the discharge -  At the start and end of rotating n=1 modes with f > 1 kHz -  At the time of maximum βN

•  LMs/QSMs often cause a decrease in βN and should not exist during time of maximum


8

Decay Rate Distribution

0.000 0.005 0.010 0.015 0.020 0.025 0.030Decay Rate (MA/ms)

0

500

1000

1500

2000

2500

3000

# of

occ

urre

nces

Distributions of the absolute value of Ip decay rate and decay time inform disruption identification

•  Disruption thresholds used lie in range [-0.03, -0.01] MA/ms -  Faster decay for analysis sensitive to false-positives -  Slower decay for analysis sensitive to false-negatives

•  ~70% of plasma shots have decay rate faster than -0.03 MA/ms •  Decay rate averaged over majority (>60%) of current drop •  Decay time calculated with nominal 1 MA current


Decay Time Distribution

0 200 400 600 800 1000Decay Time (ms)

0

500

1000

1500

2000

2500

# of

occ

urre

nces

Slow Ip decays

Highly probable disruptions

Possible disruptions

9

Automatic detection of m/n=even/1 rotating NTMs and n=1 LMs/QSMs performs well on majority of shots


Rotating NTM

LM/QSM with precursor

Born LM/QSM

Born LM/QSM

Rotating NTM

10

Automatic analysis was validated with manually analyzed shots

•  LM/QSM with rotating m/n=even/1 NTM precursor -  Disruptive: Percent false-positive < 4 %

•  50 cases •  Definition of disruptions è Ip decays < -0.02 MA/ms

–  Non-disruptive: Percent false-negatives < 8 % •  50 cases •  Definition of disruptions è Ip decays < -0.01 MA/ms

•  LM/QSM without precursor –  Percent false-positive > 30% –  These modes will not be addressed in what follows

•  Future work: reduce percent false-positives and investigate LMs/QSMs without precursors


11

Building the database: shots 122000-159838, corresponding to years 2005-2014

•  Runtime = 72 core hours to populate 37,839 shots -  Highly parallelizable: (actual runtime) = (core hours)/(# of cores)

•  Physics contained in database: –  Plasma shot? –  Plasma duration –  Ip decay rate (disruption identification) –  n=1, m=even rotating TMs:

•  End times and durations

–  n=1 LMs and QSMs: •  Start times and durations •  Probable m=2, m≠2, or m indeterminate •  With or without rotating precursor •  Time-resolved amplitude and phase (Δt=2 ms)

–  Maximum βN


12

0 100 200 300 400 500Slow Down Time (ms)

0

50

100

150

# of

occ

urre

nces

75% of m=even, n=1 islands rotating at 2 kHz lock within 80 ms

•  Time from f = 2 kHz to locking -  2 kHz is chosen empirically: most NTMs that slow to 2 kHz will lock -  Possible to better inform this decision with wall-torque physics

•  Most frequent slow down time = 47 ± 10 ms


75%

13

Disruptive n=1 LMs/QSMs with precursors most frequently survive for 300 ± 100 ms

Survival Time Distribution

0 1000 2000 3000 4000Survival Time (ms)

0

20

40

60

80#

of L

M/Q

SM w

ith P

recu

rsor

Eve

nts

•  Lifetime of LM/QSM from first appearance to likely disruption -  only LMs/QSMs in discharges that terminate with fast Ip decay (likely

disruption) are considered here

•  ~75% survive between 150-1010 ms


75% (top-down integration)

14

Nondisruptive LMs/QSMs with m/n=even/1 TM precursors

0 500 1000 1500 2000

6

8

10

12

B r (G

) of L

M/Q

SM

0 500 1000 1500 2000Time (ms) after n=1 LM/QSM appearance

0

500

1000

1500

# of

LM

s/Q

SMs

0.5

1.0

1.5

2.0

2.5

3.0

log 1

0N

Non-disruptive LMs/QSMs with precursors: 75% have Br

ext < 10 G and τ < 400 ms


75%

75%

•  Modes may decay naturally, spin up, or decay by operator intervention (often Ip ramp down)

15

Disruptive LMs/QSMs with m/n=even/1 TM precursors

0 500 1000 1500 2000

6

8

10

12

B r (G

) of L

M/Q

SM


0200400600800

10001200

# of

LM

s/Q

SMs

0.5

1.0

1.5

2.0

2.5

log 1

0N

Disruptive LMs/QSMs with precursors: 75% have Br

ext < 11 G and τ < 820 ms


75%

75%

•  Disruptive modes are 10% larger than non-disruptive •  Disruptive modes “live” twice as long as non-disruptive

16

Disruptive n=1 LMs/QSMs with precursors: 75% disrupt with Br < 15 G


•  Modes disrupt with Br ~1.5 times larger than before disruption

•  Qualitative agreement with 75% of modes having τ < 820 ms (slide 14) is seen

Above: Br averaged from -24 to -16 ms before disruption. Each point represents one disruptive n=1 LM/QSM with precursor

0 1000 2000 3000 4000 5000Survival time (ms)

0

10

20

30

40

B r (G

) of n

=1 L

M/Q

SM b

efor

e di

srup

tion

Single LM−QSM75% upper−bound

17

Disruptive LMs/QSMs with TM precursors


6

8

10

12

B r (G

) of L

M/Q

SM

0.51.01.52.02.5

log 1

0N

•  Larger n=1 LMs/QSMs show faster growth •  Modes saturate between 50-100 ms •  Only modes with survival time > 200 ms shown

Mode growth and saturation seen in first 100 ms of lifetime


0.2 G/ms

1 G/ms

saturation

18

Greater than 22% of disrupted shots end with a “LM/QSM with precursor” present


•  Disruption definition è Ip decay < -0.03 MA/ms -  Percent false-positives < 4% (50 cases manually

validated) •  One detected false-positive caused by

disruption at ~50% current ramp-down

-  Shots that disrupt during current ramp-up included (not considered errors)

•  Fraction of disruptions with “LMs/QSMs with precursors” is likely greater

–  Percent false-negatives is unknown to date

•  Only shots where all necessary data are available are included here

–  This subset constitutes ~75% of all plasma shots

Disruptions with LM/QSM

with rot. prec.,

920, 22% Disruption without

LM/QSM with rot. prec., 3234, 78%

19

Summary of n=1 analysis


•  A LM/QSM database has been populated with 18,500 analyzable

shots

•  Automatic analysis validated with manually analyzed data

•  75% of m=even NTMs have a “slow down time” of < 80 ms

•  Results of n=1 LMs/QSMs with precursors:

-  75% have a “top-down integrated” survival time between 150-1010 ms

•  75% have a survival time < 820 ms when integrated from left

-  Disruptive LMs/QSMs have 10% higher Br and live 105% longer than non-

disruptive LMs/QSMs

-  During onset, larger modes exhibit faster growth

-  Modes appear to saturate in ~50 ms

-  Greater than 22% of disruptions contain LMs/QSMs with precursors

20

Future work:


•  Reduce the percent of false-positives of LMs/QSMs without

precursors and compare to those with precursors

•  Analyze LM/QSM time-resolved phase to differentiate LMs from

QSMs and then compare these modes

•  Investigate dependences of LM and QSM properties on

plasma parameters such as βN

•  Quantify the efficacy of LM and QSM steady-state mitigation

techniques including ECCD at q=2 surface, reduction of NBI

power, and mode entrainment

statistical analysis of locked modes and their...

Documents