runaway electron losses enhanced by resonant magnetic...

/13G. PAPP IAEA Meeting on Energetic particles 2011-09-10 1

Runaway electron losses enhanced by resonant magnetic perturbations

G. Papp1,2, M. Drevlak3, T. Fülöp1,P. Helander3, G. I. Pokol2

1) Chalmers University of Technology, Göteborg, Sweden2) Budapest University of Technology and Economics, Budapest, Hungary3) Max-Planck-Institut für Plasmaphysik, Greifswald, Germany

/13G. PAPP IAEA Meeting on Energetic particles 2011-09-10

Introduction• Runaway electrons generated in disruptions pose a

serious threat on large devices• Resonant magnetic perturbations (RMP) significantly

alter the magnetic structure and transport of tokamaks• The undesired population of high energy runaway

electrons can be lowered by RMP in experiments

2

G. Papp et al, Nuclear Fusion 51 043004, 2011.G. Papp et al, PPCF 53 095004, 2011.

➡ RMP can influence the low-energy edge runaways➡ Large amount of runaways can be removed in ITER➡ An effective RMP configuration was identified

http://stacks.iop.org/NF/51/043004


http://stacks.iop.org/PPCF/53/095004



Modelling of RMP• Resonant Magnetic Perturbation (RMP) is a possible

method to reduce the number of runaway electrons• Promising, but inconclusive experimental results1,2

• Theory suggest that dB/B=0.1% is enough to suppress the avalanche generation3

• Runaway transport in perturbed fields is very complex➡ 3D numerical modelling is required

• Solving the complete kinetic problem requires tremendous computational power

• Approximation: test particles in predefined 3D fields

3

[1] M. Lehnen et al, PRL 100 255003, 2008.[2] V. Riccardo et al, PPCF 52 124018, 2010.[3] P. Helander et al, PoP 7 4106, 2000.


• Relativistic drift equations to follow the particle propagation in 3D EM fields

• Extended version of the ANTS (plasmA simulatioN with drifT and collisionS) code4

➡Collisions with background plasma are calculated with an MC collision operator valid for arbitrary energies5

➡Synchrotron and Bremsstrahlung radiation losses➡Cartesian coordinate system for the highest flexibility and

accurate treatment of arbitrary magnetic fields

4

Modelling of RMP

[4] M. Drevlak, ECA 33E P4.211, 2009.[5] G. Papp et al, Nuclear Fusion 51 043004, 2011.




Modelling for TEXTOR • TEXTOR-like plasma + Dynamic

Ergodic Divertor (DED) system➡ n=2 DC configuration superposed

on the VMEC equilibrium field➡ dB/B=0.1% up to !=0.8 @6kA➡Edge ergodic zone at ! > 0.8

5

+I -I

DED

Magnetic Poincaré, IDED = 6 kA

(3,2)

(4,2)(5,2)

0.1%F.-Average dB/B

0.50.60.70.80.91.01.11.21.3

0.0 0.2 0.4 0.6 0.8 1.0Radial position (normalized flux)

103X

(dB/B

)2flu

x

IDED=6kA

Ergo

dic

Islands


• Increasing energy ➡ runaway population is shifted towards the LFS ➡ causes significant losses regardless of the DED

• Effect of RMP decreases with increasing particle energy

Drift topology ≠ magnetic topology!

Core is intact


Loss enhancement• Low energy (~1 MeV) particles closer to the edge

(!>0.7) are affected➡Particle losses initiate sooner,

similar loss dynamics➡At higher energies the

difference is negligible➡Runaway current damping rate

is the same order as in experiments• Simulations did not explain the loss

of core- and high energy electrons• It may be explained by MHD instabilities onset by the

disruption6 - in small tokamaks

7

0

20

40

60

80

100

2 2.2 2.4 2.6 2.8 3 3.2 3.4

% o

f p

arti

cle

s lo

st

time [ms]

0 = 0.7

Etor = 14 V/m

Einit = 1 MeV

IDED

= 6 kA

IDED

= 0 kA

RM

P O

N

RM

P O

FF

[6] V. Izzo et al, Nuclear Fusion 51 063032, 2011.


Runaway losses in ITER• ITER inductive scenario #2, IP=15 MA

➡RMP with the ELM perturbation coil system (9 X 3 coils)

➡ n=3 and n=9 perturbations withdB/B=0.1% up to !=0.5

• n=3 creates broader islands, hence,is more effective - 4 configs. tested

8

++

-

+

+

-

+

+-

0.20.40.60.81.01.21.41.61.82.0

0.0 0.25 0.75 1.0Radial position (normalized flux)

IRMP: 60 kA

0.1%

n=3 (all)n=9 mid-reversed

n=9 basic

Averaged dB/B

10 x

3(d

B/B

)2flu

x

0.5

n=3

n=9

n=9 ‘R’


Magnetic Poincaré

(a)

- -+

+ --

-- +

Particle Poincaré (10 MeV)

(c)

Magnetic Poincaré

(b)

-

-

-

++

++

++

Particle Poincaré (10 MeV)

(d)

2 out of the 4 configurations is shown

Aligned Non-aligned

Stochasticity Islands


Confinement volume shrinkage• Losses due to energy gain• Up to 50% shrinkage for

10 MeV particles(10% without RMP)

• Up to 60% for 100 MeV>50% without RMP➡RMP is less effective

for high energies➡Not many particles

reach up to 100 MeV• “B” is the best configuration7

10

01020

30

40

50

60

% o

f con

f. V.

shr

inka

ge

Etor = 0 V/m IRMP = 60 kA

n=3 "A"n=3 "B"n=3 "C"n=3 "D"

UNPERT.

10-3 10-2 10-1 100 101 102 103 01020

30

40

50

60

% o

f con

f. V.

shr

inka

ge

time [us]

Etor = 0 V/m IRMP = 60 kA

n=3 "A"n=3 "B"n=3 "C"n=3 "D"

UNPERT.

10 MeV

100 MeV

[7] G. Papp et al, PPCF 53 095004, 2011.




Time-dependent electric field• Taken from simulations of the evolution of the radial profile

of the current density and the diffusion of the electric field8

11

[8] H. M. Smith et al, PPCF 51 124008, 2009.

(b)


Loss enhancement• ~ 11 ms until 100% loss for particles launched at !0=0.7• With RMP, losses start at 1µs, 100% loss by 0.1 ms

➡ Logarithmic loss dependence on time: Nlost ~ log(t)➡ Loss initiation depends exponentially on !0➡Particles within !<0.5 are practically untouched

12

log. axis!

0

20

40

60

80

100

10-3

10-2

10-1

100

101

102

% o

f p

arti

cle

s l

os

t

time [ms]

Etor (t)

Einit = 1 MeV

n=3 'B', 60kA

=0.7

=0.6

=0.5

Log(t) fit

RMP ON

=0.7

=0.6

=0.5

0

20

40

60

80

100

9.8 10 10.2 10.4 10.6 10.8 11 11.2

% o

f p

arti

cle

s l

os

t

time [ms]

= 0.7

Einit = 1 MeV

IRMP = 0 kA

RMP OFF

=0.7


Conclusions• Identified a possible RMP configuration for runaway

suppression in ITER➡RMP enhances the edge (!>0.5) particle transport that

significantly increases particle losses ➡Particles get lost while still at low energies

• Can be applied along with other mitigation methods(e.g. pellet or gas injection)

• Fast losses reduce the seed population for avalanchebut might increase the electric field

• Self-consistent calculation of the runaway dynamics is feasible with the ARENA+ code in the near future

13

G. Papp et al, Nuclear Fusion 51 043004, 2011.G. Papp et al, PPCF 53 095004, 2011.





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