7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Staged cooling of a fusion-grade plasma in a tokamak thermal quench
Jun Li1, Yanzeng Zhang2, Xianzhu Tang2
1
Department of plasma physics and fusion engineering, University of Science and Technology ofChina,
2
Theoretical Division, Los Alamos National Laboratory
e-mail (speaker): junlisu@ustc.edu.cn

Plasma thermal quench (TQ) is a rapid cooling process
project at Los Alamos National Laboratory (LANL)
Nucl. Fusion(2023)
066030 are exposed to external cold
J. Li et aloccurringwhen63hot
plasmasunder Contract No. 89233218CNA000.
energy sinks. The core of TQ is the fundamental
transport
which hasbroad aappeal
to plasmaTe! (x = 0, t)
fieldphysics
lines suddenlyintercepts
cold boundary,physicists
a varietyspecializations.
In tokamak
barelywith
changesover aofperiodthat is approximately
one-thirdτtre . Thislike
is simply
the time
the so-calledfusionofreactors
ITER where
hotforplamas(T~100precooling
front(PF), which
is drivenbybystrong
suprathermal
electronmillionKelvin)are confinedmagnetic
fields,loss andfrom theareboundary
towardcore plasma at awhen propagatesthe confinements
disrupted
eithertheintentionally
speed UPF = 2.4v
, to arrive
the plasma(x =0) [23].
or unintentionally,
TQth0occurs
andatmarks
the center
point of"noThis
instance
markedreleaseby the fromblack hotdashedverticalreturn"of therapidisenergy
plasmasto line infigure
2. Thewalls.
subsequentcooling ofTe!significantly(x = 0) is indeed driven
the coldreactorThis process
canby
the
electronconduction
flux
thata similar
bring thermal load management issue at follows
the walls
and scalingastheflux
limiting
form
inequation(2).
Noticepotentially cause severely damage to the reactors. that for anearly collisionless plasma, the conduction
corresponding´ broad flux
Despitethe crucial role of TQ and theinterests
ofto Te! cooling is given by qen ≡ me ṽ3! fe d3 v. Consequently,
fundamental transport physics, previous understandings
the duration of this phase does follow the free-streaming scalhave been
failed to predict or explain many TQ-relevant
ing previously given in equation (3). Remarkably the precursor
experimental
measurements,in theparticular
theprecoolingbroad trailingphase ends
abruptly when
so-called
variationofTQ
times.
front (PTF) reaches the center. This is a second electron front
Here weour from
theoreticaland numerical
study
thatpresent
propagates
the boundary
toward thecoreofplasma,!
Figure 1. Te|| (x = 0, t) of a slab plasma (x ∈ [−LB, LB])
TQ physics,in
which
we
find
surprisingphysics
scalings
with a speed UPTF = 2e∆ΦRF /me [23]. Here the reflecting Figure 2. Te! (x = 0, t) of a slab plasma (x ∈ [−LB , LB ]) from a
VPIC simulation
withDeL, Bwhere= 700λwhereλDe isand uniquetransport
characteristics
thatambipolar
will improve
our field fromVPICasimulation
with LB = 700λλDeDeis,theelectron
potential∆ΦRF isthe result of theelectric
theinitialelectron
Debyelength.
The
initialplasmaisDebyelength.
The
initialplasmaisuniform
withm/m=1/100,ei
understandings
the TQlayer
physics
anda experimental
in the ion torecession
whereplasma rarefaction wave
Z = 1 andwith
Kn,0 electron= 98 and thethermobathboundary
ontwoends hasuniformandion
mass
ratio
m/m
=1/100,eiresults.
disruptions
wherewith
the Te! , we T = 0.01T . The vertical dashed lines mark the moments when theis Specifically,formed. Sincein
thetokamak
ambipolarpotential scalesw
charge 0state Z = 1 and Knudson number K slopes
= 98
would
normally havevth,becomes
UPF , and thus
∆t1 ∼ τtre . ion
magnetic
connection
lengthcomparable
to ore < UPTF <four fronts reach the center, while the dotted lines with n,0of −2
theandthermobathboundaryends has
The short
durationof the precursor
phase produces(blue)−2/5 (green)
are markedon
fortwothe cooling
flow phaseeven shorter
thanthe plasmamean-free-path,parallelvery lim- and(∆t2 ) and collisional
phase 0(∆ttemperature
Tw = 0.01T, whereT0 is the initial plasma
ited cancoolingand typically
T1 ! 0.6T. the thermal4 ).
transport
dominatethe energy
loss0andCooling
flowplasmaphase (TT 1 tofour
T 2 with
Tw < T2 # T0 temperature. The vertical dashed lines mark the moments
e! fromquench ofthe coregoesthroughphases
andthat∆t2have∼ τtri distinct): Once thePTFs reachranges
the plasma
the four fronts (two electron fronts followed by(stages)
temperatureand center from whenIn the limit of significant plasma cooling, one can write Ve! ≈bothends,
qundergoes
aqualitativetransition
fromscaltwoionfronts) reach the center, while the dotted lines
endurations [1]. The main temperature drop occurs while(−VL + VR ) /2 and find a convective energy flux scaling foring
withv
(i.e.
q∝nvT)
toscalingwithV(i.e.
th,eeneth,ee!
i!
withslopesof −2conduction(blue) and −2/5 (green) are marked forthe core plasma remains nearly collisionless, with theelectron thermal
qen ∝ ne Vi! Te! ). Here Vi! is the parallel ion convective flow the collisionless cooling flow phase and collisional
parallel electron temperature Te|| dropping in time t as Te||and ambipolar transport implies the parallel electron flow phase.
6Te!
∝ t-2Vand≈aVcoolingtime that scales with the ion soundqen ≈ne Ve! Te! .
(4)
e!
i! . Previously we have shown that in a semi-infinite
5T0wave plasmatransit time
overthelengthoftheopenmagnetic
bounded at one side only by a thermobath boundary,field line[2]. Thesesurprisingphysics
scalings are
qen always
has thefree-streaming
flux-limiting
formthene vth,e Te! In a cooling plasma of Te! # T0 , one recovers the remarkable
result dueof effective
suppressionof parallelto the cold
electrons being
pulledelectron
into the hot plasma result of qen # ne Ve! Te! observed in VPIC simulations.
thermalin anotherwisebounded,by conduction
the ambipolarelectric
field [23].
The qualitative change
An even more interesting and impactful result is on qen ofquasineutral,collisionlessplasma,
which
is differentof qen inanda bounded
plasmais drivenby how
Te! is being a plasma with thermobath boundary conditions. The subtlety
from what
to date on electron
cooledarein known
a long mean-free-path
plasmathermal
where electron trap- is that cold electrons from the boundary plasmas can follow
ping isalongprovided
the reflecting
conduction
the bymagnetic
field (ambipolar)
in a nearly potential along the ambipolar electric field into the core plasma. This cold
References
the magnetic
field line on bothends.We also find thatelectron beam component was previously found to restore thecollisionlessand quasineuralplasma.
[1]
Zhang, Y.,flux-limiting
Li, J., & Tang,(2023).(2)Cooling
-2/5
The
core
cooling
physicsismoststraightforwardly
underfree-steaming
form X.-Z.
of equation
in a semiTe||∝ t in the collisional stage. All the aboveflow
regimeofa
plasmathermalquench.
EPL
141,
stoodinaplasma
withperfectly
absorbingboundaries.
Since
infinite
plasma
[23].
With
cold
boundary
plasmasonboth ends!
theoretical results are supported by our fully-kinetic
the trapped-passing boundary is given by vc ≡ e∆ΦRF /me , 54002.
atx=±L,thecold
electronbeams
frombothsides,
accelerBparticle-in-cell simulations [Figure 1].
J., Zhang,Y.,electric& Tang,
X.-Z.
(2023).
and the truncated electron distribution at x = 0 has the form [2]ated Li,by theambipolar
field,
nearlycancelStaged
each other,
This work is jointly supported by U.S."Department# " of#in the electron
flow and thermal
conduction
flux. Asthermal
the result,coolingof a fusion-gradeplasmain a tokamak
v! Office ofv!
2n0Fusion−(EnergyEnergy fOfficeofSciences
andv2! +v2⊥ )/2vth0eΘ
1−
Θ
1+,
q
takes
onthequalitatively
different
resultbyretaining
the0=quench.
NuclearFusion
63,066030.
envc(2π)3/2 v3th0Computing Research under
Advanced Scientific
the vcconvective energy transport scaling in the absorbing wall case.
Tokamak Disruption Simulation (TDS) Scientificwith Θ(x) the Heaviside function satisfying Θ(x < 0) = 0 and Quantitatively, once the ion recession front, which propagates
Discovery through Advanced Computing (SciDAC)
from the boundary to the plasma center at the local ion soundΘ(x > 0) = 1. One´ can see that ´the parallel$ electron%temperature Te! (vc , T0 ) = me ṽ2! fe d3 v/ fe d3 v = v2c /3v2th0 T0 of theelectrostatically trapped long mean-free-path electrons cools
drastically with a decreasing vc /vth0 # 1. This correlates witha reducing reflecting potential ∆ΦRF . Away from the symmetry point at x = 0, a finite parallel electron conduction flux
arises from the asymmetric truncations (V L and V R ) on the positive and negative sides of electron distribution in v!

speed, reaches the center, qen has settled into a magnitude thatis solidly subdominant to the actual convective energy flux
3ne Vi! Te! , as shown by the black lines in figure 3(e).
Remarkably the core plasma cooling history in the cooling flow phase is similar if not nearly identical between theabsorbing and thermobath boundary cases. This is connected to thermal conduction being subdominant to convectiveenergy transport in both cases. Next, we use the absorbing