Simulation of disruption mitigation under massive gas injection in tokamak KTM

1
Simulation of disruption mitigation under
massive gas injection in tokamak KTM
A.Mineev1, M.Sugihara2, K.Lobanov1, L.Makarova1,
V.Vasiliev1 1D.V.Efremov Institute, Russia
2ITER International Team, Japan
JOINT MEETING OF THE 3rd IAEA TECHNICAL MEETING
ON SPHERICAL TORI AND THE 11th INTERNATIONAL
WORKSHOP ON SPHERICAL TORUSSt. Petersburg State
University, St. Petersburg, RUSSIA 3 to 6
October 2005
2
Introduction

• For plasma current quench stage electromagnetic
  pressure pv on in-vessel components of a tokamak
  is scaled as pv ? IP2/?cq, where IP is plasma
  current before disruption and ?cq is plasma
  current decay time. So, search of methods of EM
  loads mitigation, especially possibilities of
  current quench time increasing is important.
• Value ?cq usually is defined by the rate of
  plasma current magnetic energy dissipation due to
  impurity radiation. It is supposed that large
  amount of impurities comes into the plasma during
  thermal quench stage (basic case of disruption)
  or after massive gas injection from gas jet
  reservoir (noble gas injection for plasma
  mitigation).
• Model for description of plasma current behaviour
  IP(t) must include
• plasma resistance model (include elastic and
  nonelastic collisions with
• electrons and neutrals)
• impurity radiation model (full
  collisional-radiation model)
• generation of runaway current (include Dreicer
  and avalanche
• generation).
• Report is devoted mainly to the study of plasma
  current decay problems after impurity gas
  injection in KTM tokamak with use of DIMRUN model.

3
1 DIMRUN 0D code description
For analysis of the process of plasma current
shut down after impurity injection 0D code
DIMRUN was developed (Dynamics of IMpurity
radiation and RUNaway generation in
tokamaks). Three sorts of impurities are taken
into account carbon and noble gases neon and
argon. Carbon impurity corresponds to non
mitigated case. Mitigation is analysed with Ne
and Ar injection. 1.1 Energy balance
equations System of equations includes balance of
thermal energy and magnetic energy.
Here QOH (IP-IR). Ures is ohmic heating power,
Qz is radiation power Q? is energy exchange
term between electrons and ions, ni is total
concentration of ions, VP is plasma volume
UresRPL.(IP- IR) is active plasma loop voltage,
RPL ?e.2?Ro/(?ka2) is plasma resistance, E
Ures/2?Ro is vortex field on the plasma loop, ?e
is plasma resistivity, IR is runaway current,
?Ee, ?Ei are energy losses due to disturbance of
magnetic field during impurity injection.
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1.2 Plasma resistivity model
Total plasma resistivity is a sum where of ?ei
correspond to elastic electron-ion collisions,
?ea to electron-atom collisions and ?en to
nonelastic electron collisions (which lead to
ionisation, excitation, recombination etc.).
Elastic e-i collisions ?ei ? ?Coulomb ?
10-4.Cs,CZeff. ln?/Te1.5 ?.m, eV Elastic
e-a collisions
where
lt?H0vgt, lt?z0vgt for hydrogen and impurities (C,
Ne, Ar) are obtained from experimental values.
Inelastic e-a, e-i interaction Below inelastic
collisions means processes of interactions of
electrons with atoms and ions, which results in
transition between energy levels (ionisation,
recombination, excitation). Inelastic collisions
gives following contribution to plasma
resistivity where Ij and Rj are rate
coefficients for ionisation and recombination ?H
, ?jZ correspond to energies of ionisation and L
is a function of radiation.
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1.3 Impurity radiation model
Model of dynamics of ionisation state of
impurities is used for simulation of impurity
ionisation states evolution nj(t). It includes
the following set of equations dn0/dt
-nen0I0 ne.n1R1 nH0n1X1 Sz dnj/dt
nenj-1Ij-1 - nenj(Ij Rj) nenj1Rj1
nH0 (nj1Xj1-njXj), j1...Z-1 dnz/dt
nenz-1Iz-1 - nenzRz nH0nzXz
where n0, nj is concentration of neutral and jth
ionized ion nH0 is concentration of neutral
hydrogen Ij, Rj and Xj are rate coefficients for
ionization, recombination and charge
exchange. Radiation power for impurity can be
represented as a sum of contribution from all
ionisation states where Uk are radiation
coefficients.
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1.4 Runaway model for electrons
If during disruption electrical vortex field E
is high enough, runaway generation takes place.
It results in appearance of runaway current by
Dreicer and avalanche mechanism of
generation. Dreicer (straight) generation
Cr11, ?ee is time between e-e collisions vTe is
thermal speed of electrons, Zeff is effective
charge, is
Dreicer field. Avalanche generation

is
toroidal modification factor, ln?ee is Coulomb
logarithm for e-e collisions,
is so called critical field for
avalanche generation,
is characteristic time between collisions
for runaway electrons. Runaway current is
IR?a2 k jr density of runaway current is
jr e nr c and for nr we have
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1.5 Thermal losses due to disturbance of
magnetic configuration
Disturbance of tokamak magnetic configuration ?B
in plasma discharge takes place during various
MHD phenomena (MHD bursts, disruptions etc.). To
above events must be added impurity injection
into the plasma. Such disturbances of toroidal
magnetic field leads to appearance of additional
powerful channel of energy losses. After reaching
the wall, this heat flux can give incoming of
impurities to the plasma periphery. Fast
penetration of impurities to the plasma center
can be also due to ?B effect. Estimation of
energy confinement time during magnetic
disturbances can be made by following way where
?eff is effective electron thermal conductivity
? v.? is free path, ? is time between
collisions and v is speed of particle. Amplitude
of magnetic disturbance ?B caused by jet can be
estimated by comparison of jet pressure ?vs2/2
and magnetic pressure (?B)2/2?0. Velocity of gas
jet is about the same both in vacuum and through
the plasma and is equal to sonic velocity vs ?
1800/Az1/2 m/s, Az is atomic mass of impurity.
From ? vs2/2 ? (?B)2/2?0 we can obtain ?B ?
nimp1/2. So, if ?B ? 3.10-4 T for nimp
0.1.1020 m-3, then ?B will be ? 3 10-3 T for
nimp 1021 m-3.
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2. Model testing on DIII-D experimental data

• . Neon gas jet injection
• Experimental data with Ne gas jet .
• no runaway current is observed
• Te falls from 1.5 keV to several eV
• density is increased up to 41020 m-3
• Neon radiation power is ? 5 GW
• Simulation was made with parameters
• IP0 1.5 MA, a0.6 m, R1.7 m,k 1.8,
• Te01.5 keV, nH0.31020 m-3, LP 2 ?H
• Neon impurity with nNe 51020 m-3
• time duration of jet injection tinj 3 ms.
• Results of simulations
• no runaway current,
• IP decay time ?L/R3 ms (1.5?0.55 MA)
• IP decay time ?cq7 ms (1.5?0.15 MA)
• Te falls down to 2 eV
• density ne increases up to 41020 m-3 .

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• Ar (pellet and jet) injection
• Experimental data for Ar injection into the
  plasma were taken for two cases
• Ar pellet with total amount of injected
  particles NAr 21020 (nAr 0.11020 m-3)
• Ar jet with NAr 41022 (nAr (15-20).1020
  m-3).
• Main peculiarity of presented experimental data
• high runaway current and soft X-ray emission for
  low Ar concentration
• absence of runaway current for high Ar
  concentration.
• Simulations give the dependence of IR (after
  establishment of plasma current shut down) on
  nAr, as shown in Table for nH ? 0.11020 m-3.
• As seen from the Table
• there is high value of IR for low Ar gas jet
  concentration. In our example for Ar pellet
  injection into DIII-D plasma with nAr 0.11020
  m-3, calculations give IR ? 0.65 MA (experiment
  IR 0.5 0.6 MA)
• there is abcence of IR for high Ar gas jet
  concentration. In our example, for Ar jet
  injection into DIII-D plasma with nAr
  (15-20)1020 m-3, IR ? 0 (as in experiment).

nAr, 1020 m-3 0.1 0.3 0.5 1 3 ? 5
Irun, MA 0.65 0.57 0.4 0.18 0.05 0
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3 DIMRUN code simulations for ITER
3.1 Results of calculations The following
initial parameters were taken for calculations
IP0 15 MA, a 2 m, R 6.2 m, k 1.7, Te0
10 keV, nH 11020 m-3, LP 7 ?H. Main
results of plasma current shut down calculations
after impurity injection (C, Ne, Ar) in ITER are
presented in Figure. These data define also
threshold impurity concentration nimp,thr, which
divide region of nimp on zones with and without
runaway current. Run
away current IR (left) and L/R time constant ?L/R
(right) vs. impurity concentration. Area with
absence and presence of runaway is shown

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3.2 Level of mitigation for ITER without runaway
generation
L/R time constant (defined here as the time of
one exponent decay in plasma current) decreases
with nimp. So, minimum values of electromagnetic
forces during disruption corresponds to minimum
available (i.e. without high runaway current)
impurity concentration. Calculations show, that
for nimp gt 5.1020 m-3 runaway current is absent
for all three analysed types of impurities C,
Ne and Ar. There is tendency of threshold
concentration nimp,thr decreasing with increasing
of impurity mass nimp,thr ? 51020 m-3 for
carbon, nimp, thr ? 41020 m-3 for neon and
nimp, thr ? 0.61020 m-3 for argon. Comparison
of L/R time constant ?L/R for given value of
impurity concentration in the range nimp gt 51020
m-3 shows, that neon impurity gives higher values
of ?L/R than carbon or argon. In ITER project
carbon impurity (from the wall during disruption)
defines basic disruption time (i.e. without
mitigation). For carbon impurity near the
boundary of runaway absence our calculations
(Fig.1) gives ?L/R(C) ? 18 20 ms. This time is
close to the predicted time constant of
exponential waveform in ITER, according to
experimental database scaling for fastest quench
disruptions. So, unmitigated value gives ?L/R ?
18 20 ms. As can be shown from Fig.1, argon is
not optimum species for mitigation, even for its
lower available concentration (for nAr gt 11020
m-3, ?L/R lt 15 ms). At the same time for neon
impurity with available concentration nNe ?51020
m-3 value of L/R time constant can reach 40 ms.
So, level of mitigation for Ne case is about two.
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DIMRUN code simulations for KTM
For ITER unmitigated time of plasma current decay
is taken as ?L/R ? 18 20 ms. This value agree
with empirical scaling for the fastest qurrent
quench time 6 ?L/R ? S ms, m2 where S ?ka2
is plasma poloidal cross section (S ? 20 m2 for
ITER). For the KTM case 8 with S?1.1 m2
(project values k 1.7, a 0.45 m), according
to empirical scaling, fastest qurrent quench time
?L/R ? 1.1 ms. This value can be taken as
unmitigation time constant in KTM. Simulations
of ?L/R for the cases of C, Ne and Ar impurities
input after thermal quench in KTM were made with
following initial parameters IP00.75 MA,
a0.45 m, R00.9 m, k1.7, Te01 keV, nH0.5.1020
m-3, LP0.7 ?H, deuterium plasma. For KTM the
same as for ITER or DIII-D cases effective value
of plasma inductance LP was lower than well known
value of total plasma inductance LP,t
?0R.ln(8R/a/k1/2) 2 li/2 (LP,t ? 10 ?H and
LP ? 7 ?H for ITER, 2.5 ?H and 2 ?H for DIII-D
and 1 ?H and 0.7 ?H for KTM) because current
quench time ?L/R is lower than characteristic
time of magnetic field diffision through vacuum
chamber.
.
13
KTM time dependences of plasma parameters after
carbon impurity input.
Time dependences of plasma parameters (Te, Ti,
IP, IR, QOH, Qz, Rpl, ln?, Ures) after carbon
impurity injection with nC 1.1020 m-3, KTM
simulations
14
Mitigation effect in KTM Main difference of
current quench behavior in comparison with ITER
is that in KTM runaway current is absent for the
whole investigated diapason of nimp. Mitigation
effect in KTM is more effective for the case of
Ne impurity, than for Ar. Carbon with density nC
? (0.7-1.5).1020 m-3 gives the same value ?L/R ?
1 ms as for empirical scaling. So, it is possible
to say about mitigation effect when nim ? 5.1020
m-3 (Ne impurity) and nim ? 0.7.1020 m-3 for
Ar impurity.
. L/R time constant vs. impurity concentration
for C, Ne and Ar, KTM simulations
15
Conclusions

• Resently DIMRUN code was developed for the
  analysis the process of disruption mitigation
  under massive gas injection in ITER.
• DIMRUN code was checked on DIIID results for the
  cases of Ne and Ar imputity injection and show
  good accordance with experiment.
• Pecularities of plasma current shut down under
  C, Ne and Ar impurity injection for ITER and KTM
  tokamak are reported.
• For ITER case there is threshold impurity
  concentration, which divide region of nimp on
  zones with and without runaway current. Argon is
  not optimum species for mitigation, even for its
  lower available concentration. Neon impurity with
  available concentration nNe ?5.1020 m-3 can give
  level of mitigation about two.
• For KTM case in all investigated region of
  impurity concentration (0.1 5).1020 m-3
  simulations predict absence of runaway current
  during current quench phase. Mitigation effect is
  more effective for the case of Ne impurity, than
  for Ar. Level of mitigation can reach several
  times.

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