1. TH/P4-1 27th IAEA FEC, Ahmedabad 22-27 October 2018
Runaway electron mitigation in ITER disruptions by injection of high-Z impurities
J. R. Martín-Solís1, E.M. Hollmann2, M. Lehnen3, A. Loarte3 and J.M. Reynolds1
1Universidad Carlos III de Madrid, Avda. de la Universidad 30, Leganés-Madrid, Spain
2University of California-San Diego, La Jolla, California , USA
3ITER Organization, Route de Vinon sur Verdon, St Paul Lez Durance, France
Disclaimer: “ITER is the Nuclear Facility INB no This paper explores physics during the plasma operation of the tokamak when disruptions take place; nevertheless the nuclear operator is not constrained by the results of this paper. The views and opinions expressed herein do not necessarily reflect those of the ITER Organization.”
Add Giorgio, move Ramon as the first.
Need database
Is Daniele shot included?

2. Outline Effect of the impurities on the runaway electrons (REs)
RE mitigation in ITER disruptions by injection of high-Z impurities

3. Effect of the impurities on the RES
Injection of high-Z impurities (by SPI or MGI) constitutes one of the most promising schemes for runaway avoidance and mitigation during disruptions
Impurities can lead to:
Densification (collisional losses with the free and bound electrons)
Synchrotron radiation losses due to the increase of the electron pitch angle because of the collisions with the impurity ions
Bremsstrahlung radiation losses

4. RE mitigation by injection of high-Z impurities
before the thermal quench (TQ)
during the current quench (CQ) phase of the disruption
onto the plateau runaway beam (RE plateau mitigation)

5. before the thermal quench (TQ)
Aim: avoiding the formation of the primary runaway seeds
The amount of impurities that can be injected is limited by the range of current quench times, tres, acceptable for tolerable mechanical loads onto the vessel and in-vessel components (exponential tres ~ 22 – 66 ms for 15 MA ITER disruptions)

6. runaway plateau currents of several MAs can be generated within this tres range (particularly for the longest CQ times, corresponding to the smallest amount of assimilated impurities)
ITER 15 MA H-mode
Ar injection
Ne injection
ITER 15 MA H-mode
(J.R. Martín-Solís et al., Nucl. Fusion 57 (2017) )

7. Ar injection
ITER 15 MA H-mode
ITER 15 MA - Ar/D2 7 kPa·m3
injection of gas mixtures (Ar+D or Ne+D) might overcome these limitations if a sufficient amount of Ar/Ne and deuterium (~14 kPa∙m3) can be assimilated in the plasma
(J.R. Martín-Solís et al., Nucl. Fusion 57 (2017) )

8. during the current quench (CQ) phase of the disruption
Aim: avoiding the avalanche multiplication of the primary seeds
- early CQ injection is in principle preferable to avoid substantial runaway avalanche
- primary seeds and amount of injected impurities are de-coupled
- CQ times, tres, must be kept within the acceptable range for tolerable mechanical loads

9. inject large amounts of Ne (Ne+D) leading to acceptable range of tres
Ar seeds before CQ (tres ~22 – 66ms)
Ne seeds before CQ (tres ~22 – 66ms)

10. Runaway electron plateau mitigation
Aim: energy dissipation of the runaway beam
impurity injection results in an increase of the critical electric field, ER, for runaway generation which, if the electric field drops below the critical field, leads to the dissipation of the runaway population

11. A kinetic treatment was presented in (P. Aleynikov and B. N
A kinetic treatment was presented in (P. Aleynikov and B.N. Breizman, Phys.Rev.Lett. 114, (2015))
(P. Aleynikov et al., IAEA 2014)
the current decay follows a marginal stability scenario in which the electric field remains close (but smaller) to the threshold field for runaway generation yielding a linear decay of the current
(B.N. Breizman, Nucl. Fusion 54, (2014))

12. (M. Bakhtiari et al. Phys.Plasmas 12 (2005) 102503)
Single particle approach for the RE dynamics:
(P. Aleynikov and B.N. Breizman, Phys.Rev.Lett., 2015; J.R. Martín-Solís et al. Phys. Plasmas, 1998)
the time evolution of the momentum distribution function, G(q, t), can be determined following the evolution of the runaway electron momentum by the single particle equation:
electric field
acceleration
collisions with the
plasma particles
synchrotron
radiation
bremsstrahlung
radiation
(M. Bakhtiari et al. Phys.Plasmas 12 (2005) )

13. Runaway distribution function (E|| < ER) :
if G0(q) is the initial distribution function (at the start of the dissipation phase, t=t0):
* q0 (q,t): initial electron momentum (at time t0) dropping to q at time t
* dq0/dq : represents the effect of the changes in the electron momentum interval, dq, during
the dissipation of the electron energy

14. Runaway density decay rate :
G0(q,0)
G(q,t) q0
q0max
qmax (t)
* G0(q) ≡ G(q,t = t0)
* q0 : initial electron momentum (at time t0) dropping to zero at time t
* q0max : maximum electron momentum at time t0

15. Runaway electron plateau mitigation in ITER:
- dissipation of plateau runaway currents in ITER by Ar injection
- 0-D modelling:
- avalanche-like initial distribution function:

16. - q0 found solving the single particle equation:
collisions with the
plasma particles
synchrotron
radiation
bremsstrahlung
radiation
electric field
acceleration
(M. Bakhtiari et al.
Phys.Plasmas 12 (2005) )
include effect of the collisions with the free and bound electrons, and with the average
and the full nuclear charge of the impurity ions:
(J.R. Martín-Solís, A.Loarte and M. Lehnen, Phys.Plasmas 22 (2015) )

17. - Collisional losses: with marginal stability scenario
(for a large enough amount of impurities, the decay of the plasma and runaway current can depart from the marginal stability condition, the values of E|| falling well below ER)

18. - at high q, G(q) keeps the avalanche like exponential shape:
- the effect of the collisions increases at low q, yielding the observed depletion of G(q)
(C. Paz-Soldan et al., Phys.Rev.Lett. 118 (2017) )
- at high q, G(q) keeps the avalanche like exponential shape:
if cosq ≈ 1 and q2 >> 1 →
(J.R. Martín-Solís et al., EPS 2016))

20. - Radiation (synchrotron + bremsstrahlung) losses:
coll.+synchr.+bremss.
low q depletion + steepening high-q region
bump formation
- high-q steepening (cosq ≈ 1; q2 >> 1):

21. coll.+synchr.+bremss.

22. Crucial issue: can the runaway beam be mitigated before significant energy is deposited on the first wall or divertor components ?
characteristic time for the vertical instabilty growth in ITER ~100 ms
injection of a few kPa∙m3 of Ar (≥ 2 kPa∙m3 ) could be a promising scenario for runaway electron dissipation during disruptions

23. Scraping-off:
DINA simulations including the plasma dynamics during CQ → current termination can be initiated
earlier than the beam has been dissipated increasing the amount of energy deposited onto the
runaway electrons
(S. Konovalov et al., IAEA 2016))
Simple 0-D description of the scraping-off (M. Lehnen):
Model of the beam dissipation and scraping-off (collisions):

24. we assume VDE with constant drift velocity:

25. injection of a substantial larger amount kPa∙m3 of Ar (≥ 10 kPa∙m3 ) might be required for runaway electron dissipation during disruptions
need: self-consistent simulation of the scraping-off and energy conversión including vertical runaway motion

26. Conclusions
The effect of the injection of high-Z impurities on the REs during different phases of the disruption has been investigated:
Impurity Injection before the TQ:
aimed to avoid RE seed formation
lower RE currents found for the shortest CQs, particularly for the case of Ne
RE beams up to ~ 10 MA for the longest CQs
mixed Ar or Ne +D injection might be efficient in controlling the RE formation for a sufficient amount (~14 kPa∙m3) of D2

27. Impurity Injection during the CQ:
to control the avalanche multiplication of the RE seed
early CQ injection of Ne could be effective if the amount of Ne injected is large enough and consistent with the range of acceptable tres (close to ~6 kPa∙m3)
RE plateau beam mitigation:
to yield the dissipation and decay of the RE current
current dissipation follows a marginal stability scenario (electric field close to the critical field, ER, and linear current decay) unless the amount of assimilated impurities is large enough

28. - Distribution function:
* depletion at low q (collisions)
* steepening at high q (radiation)
bump formation
(development of kinetic instabilities ?)
extrapolations to ITER indicate that injection of a few kPa∙m3 of Ar could be a promising scenario for RE dissipation during disruptions if the impurities can be efficiently delivered into the plasma
fast VDE of the plasma when the impurities are injected can lead to the interaction of the RE beam with the wall structures before the current is dissipated, the scraping-off of the beam increasing substantially the amount of impurities required for an efficient dissipation

29. Back-up slides
- Simplified approach to the dissipation of runaway beams, including the effect of
the collisions with the plasma particles and impurities, as well as the electron
synchrotron and bremsstrahlung radiation
* current decay rate
* evolution of the distribution function
- Current dissipation follows a marginal stability scenario (electric field close to the
critical field, ER, and linear current decay) unless the amount of assimilated
impurities is large enough
- Distribution function:
* depletion at low q (collisions)
* steepening at high q (radiation)
bump formation

30. - Even if the radiation losses have an important effect on the runaway dynamics,
overall power loss from the runaway electrons seems to be dominated by the
collisions
(E.M. Hollmann et al., Phys.Plasmas 22 (2015) )

31. Profile effects (1-D modelling):
- a 0-D model has been used. Initial peaked current plateau profiles will increase
the time required for energy dissipation, the effect increasing with the peaking
only collisions; lint0 = 2
- a uniform distribution of the impurities has been assumed. The effect of the
assimilation and penetration of the impurities has to be assessed

33. Back-up slides Kinetic treatment
(P. Aleynikov and B.N. Breizman, Phys.Rev.Lett. 114, (2015))

34. Single particle approach for the RE dynamics:
(P. Aleynikov and B.N. Breizman, Phys.Rev.Lett., 2015; J.R. Martín-Solís et al. Phys. Plasmas, 1998)
electric field
acceleration
collisions with the
plasma particles
synchrotron
radiation
bremsstrahlung
radiation
(M. Bakhtiari et al.
Phys.Plasmas 12 (2005) )

35. Simplified approach:
assuming that the time scale for the electron pitch-angle equilibration is much shorter than the momentum evolution when E|| is close to the critical field:
with
and
(P. Aleynikov and B.N. Breizman, Phys.Rev.Lett. 114, (2015))

36. Runaway distribution function (E|| < ER) :
if G0(q) is the initial distribution function (at the start of the dissipation phase, t=t0):
* q0 (q,t): initial electron momentum (at time t0) dropping to q at time t
* dq0/dt : represents the effect of the changes in the electron mometum
interval, dq, during the dissipation of the electron energy

37. the average and the full nuclear charge of the impurity ions:
- include effect of the collisions with the free and bound electrons, and with
the average and the full nuclear charge of the impurity ions:
(J.R. Martín-Solís, A.Loarte and M. Lehnen, Phys.Plasmas 22 (2015) )

38. - Critical field for runaway generation (ER):
* Collisions only:
* Collisions + synchrotron
radiation (ERsynch):
Ar injection
based on analysis of dq/dt = U(q)
(P. Aleynikov and B.N. Breizman,
Phys.Rev.Lett. 114, (2015))
* Collisions + synchrotron +
bremsstrahlung radiation (ERbremss) :
based on analysis of dq/dt = U(q) 38

39. Runaway density decay rate :
where
* G0(q) ≡ G(q,t = t0)
* q0 : initial electron momentum (at time t0) dropping to zero at time t
* q0max : maximum electron momentum at time t0

40. if the amount of impurities is large enough, the evolution of the plasma
and runaway current during the decay can depart from the marginal
stability condition, the values of E|| falling well below ER

41. - at high q, G(q) keeps the avalanche like exponential shape:
- the effect of the collisions increases at low q, yielding the observed depletion
of G(q)
(C. Paz-Soldan et al., Phys.Rev.Lett. 118 (2017) )
- at high q, G(q) keeps the avalanche like exponential shape:

42. - Synchrotron radiation losses:42

43. - low q depletion + steepening high-q region → bump formation
- high-q steepening (cosq ≈ 1; q2 >> 1):

45. - Bremsstrahlung radiation losses:
high-q steepening increases:
bremsstrahlung dominates when:

46. Nevertheless:
- a 0-D model has been used. Initial peaked current plateau profiles will increase
the time required for energy dissipation, the effect increasing with the peaking
(1-D modelling)
only collisions
lint = 2

47. assimilation and penetration of the impurities has to be assessed
Nevertheless:
- a 0-D model has been used. Initial peaked current plateau profiles will increase
the time required for energy dissipation, the effect increasing with the peaking
1-D modelling
only collisions; lint = 2
- a uniform distribution of the impurities has been assumed. Effect of the
assimilation and penetration of the impurities has to be assessed
- DINA simulations including the plasma dynamics during CQ → current termination
can be initiated earlier than the beam has been dissipated increasing the amount
of energy deposited onto the runaway electrons
(S. Konovalov et al., IAEA 2016))
(include the effect of scraping-off: a(t))

48. assimilation and penetration of the impurities has to be assessed
- a uniform distribution of the impurities has been assumed. Effect of the
assimilation and penetration of the impurities has to be assessed
- DINA simulations including the plasma dynamics during CQ → current termination
can be initiated earlier than the beam has been dissipated increasing the amount
of energy deposited onto the runaway electrons
(S. Konovalov et al., IAEA 2016))
(include the effect of scraping-off: a(t))

49. assimilation and penetration of the impurities has to be assessed
- a uniform distribution of the impurities has been assumed. Effect of the
assimilation and penetration of the impurities has to be assessed
fixed impurity profile
0.5 kPa∙m3

50. lint0= 1

51. lint0= 1
lint0 = 1

52. impurity transport
Dz = 5 m2/s
lint0 = 1
lint0 = 1

53. lint0= 1
Dz = 0
Dz = 0
Dz = 5 m2/s
Dz = 5 m2/s