Transcript PIC simulations of the propagation of type

PIC simulations of the propagation of type-1
ELM-produced energetic particles on the SOL of
JET
D. Tskhakaya1,*, A. Loarte2, S. Kuhn1, and W. Fundamenski3
and Energy Physics Group, Association Euratom – ÖAW, Department
of Theoretical Physics, University of Innsbruck, Innsbruck, Austria
2EFDA, Close Support Unit Garching, Max-Planck-Institut fuer Plasmaphysik,
D-85748 Garching bei Muenchen, Germany
3UKAEA Fusion, Association Euratom-UKAEA, Culham Science Center,
Abingdon, United Kingdom
*Permanent address: Institute of Physics, Georgian Academy of Sciences,
Tbilisi, Georgia
1Plasma
Outline of the Talk
•
•
•
•
•
Introduction
Characteristics of the codes EDGE2D-NIMBUS and BIT1
Results of test simulations
Results of ELM-free and ELMy SOL simulations
Conclusions
D. Tskhakaya et. al., 9th EU-US Transport Task Force Workshop Córdoba, Spain, (2002)
Introduction
• Investigation of the energy and particle transport inside the SOL
during ELM activity is an extremely important topic, especially for
predicting the heat loads on the divertor plates of next-generation
fusion devices [Loarte et al., 2000, 2001].
• The short time scale of the process and the low collisionality of the
ELM-produced highly energetic particles define the kinetic nature
of ELMy transport.
• Despite its importance, kinetic simulations of the ELMy SOL are
rare. Simulations done up to now use either simplified linear
profiles for neutrals [Tskhakaya, et al., 2001], or do not consider
them at all [Bergmann, 2002]. Hence, they correspond to very
simplified SOL models with low recycling.
2 D Modelling of the Plasma Edge of
Fusion Devices (EDGE2D, B2-Eirene)
• The plasma edge is modelled with 2-D Fluid (plasma) + 2-D
Monte Carlo Codes (neutrals)
2-D Fluid equations
A
    ||    A  Sources  Sinks
t
A : Density, Momentum and Energy (e-, D+, Z+).
Particle, momentum, energy of the neutrals computed with
Monte Carlo Codes (Nimbus, Eirene)
Fluid + Monte Carlo are iterated to convergence
Advantages of 2-D Modelling of EDGE Plasmas
• Realistic 2-D geometry
• Fully time-dependent & consistent plasma solution with
sources and sinks
Disadvantages of 2-D Modelling of EDGE Plasmas
• Fluid approximation is not fulfilled in many interesting
edge plasma conditions (ELMs, hot ions in SOL, etc.)
ELMs are modelled by increasing cELM, DELM ~ (10 - 1000) x c0, D0
during tELM in pedestal & SOL
Experiments  lp@ELM ~ (1 - 2) lp@between ELMs
ELM simulation for ITER with B2-Eirene [Loarte, 2000]
9
8 10 7
3.00 10
9
7 10 7
9
6 10
7
2.50 10
5 10
7
2.00 10
9
1.50 10
9
4 10 7
3 10 7
5.00 10
8
0.00 10
0
2 10 7
-0.2
1 10 7
0
0
0.2
0.4
0.6
Distance from Separatrix at Divertor (m)
0.8
9
8 10 7
3.00 10
9
7 10 7
2.50 10
9
6 10 7
2.00 10
9
1.50 10
9
5 10 7
4 10 7
3 10 7
1.00 10
9
5.00 10
8
0.00 10
0
2 10 7
-0.2
1 10 7
0
0
0.2
0.4
0.6
Distance from Separatrix at Divertor (m)
0.8
)
9
3.50 10
-2
1.00 10
-2
3.50 10
Parallel Power Flux @ ELM (W m )
-2
Pedestal + SOL
-2
Parallel Power Flux between ELMs (W m )
Parallel Power Flux @ ELM (W m )
Pedestal only
Te
Radiation
Te @ ELM
Radiation @ EL
PIC code BIT1
 The 1d3v (one space and three velocity dimensions) code BIT1 was
developed on the basis of the XPDP1 code from Berkeley.
 During the simulation the motion of a large number (up to some 106)
of ions and electrons is followed:


d  qi   
Vi 
E  Vi  B ,
dt
mi

d 
X i  Vi , i  1, 2,  , N,
dt

E  ( E x , 0, 0) .

Nonlinear Coulomb and chargedneutral particle collisions
 2x  

, E x   x .
0
Coulomb collisions and charged-neutral particle collisions are
modelled via a binary collision model, so that the total momentum
and the energy is conserved during a collision :
Choosing random pairs
Colliding particles

At present the code does not follow neutrals, and assumes fixed
neutral density and temperature profiles.

All (relevant to the SOL) charged-neutral particle collisions
between hydrogen isotopes are implemented:
Elastic
A+e -A+e
Excitation A + e - A* + e
Ionization A + e - A+ + 2e
10
1
10
0
10
-1
10
-2
10
10 -18 m2
10 -20 m2
2
10
Elastic
A + A+ - A + A+
Charge-exchange A + A+ - A+ + A
A = H, D, T
ionization
elastic collision
excitation
10
1
10
0
elastic
charge exchange
-1
0
10
2
E [eV]
10
4
10 -3
10
10
-1
E [eV]
Charged-neutral particle collision cross-sections
10
1
10
3
 Secondary electron emission is implemented in the code.
Secondary electron emission due to electron impact
 e   0


E
exp 2  2 E / E0 ,   1 / cos , if   60 , else   2
E0
For graphite E0  300 eV ,
 0  1.
Secondary electron emission due to ion impact [Diem, 2001]
 i   V m / s 106  0.18,
if V  1.8  105 m / s ,
 i  0,
if V  1.8  105 m / s .
1
e
0.8
0.7
0.6
i
0.5
0.6
0.4
0.4
0.3
0.2
0.2
0.1
0
0
1000
E [eV]
2000
0
0
400
V [km/s]
800

B
Divertor
plate
Particle
source
Divertor
plate
x
Simulation geometry

During the simulation, the Maxwell-distributed electrons and ions
are injected into the source region. Particles reaching the divertor
plates are absorbed.
 In the PIC simulation neutral density and temperature profiles are
used from the corresponding fluid simulations.
Fluid simulation
Neutral density and
temperature
PIC simulation
Test simulations
• Sheath effects play an important role not only in the ELMy but
also in the ELM-free SOL
Source effect
5
4
x 10
3
qx [W/m2]
2
1
0
-1
PIC
Spitzer (Sp.)
Sp.+sheath
-2
-3
-4
0
1
2
3
4
x [m]
5
6
7
Electron heat flux profile from PIC, and corresponding SpitzerHärm and the Spitzer-Härm + “sheath” heat fluxes. ne=130.
ELM-free and ELMy SOL simulations
Mismatch between fluid and kinetic (PIC) simulations

It is necessary to shorten the simulated SOL (scaling has to
be conserved).

During the PIC simulation the plasma density and
temperature at the source cannot be controlled directly.
Input parameters are the particle source intensity and the
temperature of injected particles.

Source effect: There are peaks in the density and the
temperature profile.
• the absence of sheath in the fluid simulation results in a
higher plasma density at the wall than in the PIC
simulation. Hence, in order to have a similar chargedneutral collisionality in the PIC simulation it is necessary
to shift the neutral density (obtained from the fluid
model).
18
12
x 10
10
n (fluid)
N
n (fluid)
i
n (PIC)
i
n (PIC)
8
N
6
4
2
0
0
5
10
x [mm]
15
Two sets of simulations have been made for low and
high recycling SOL
3
x 10
Low recycling ELM-free SOL
19
Fluid
PIC
n [m-3]
2.5
Ti Fluid
Te Fluid
Ti PIC
Te PIC
250
T [eV]
200
2
150
1.5
100
1
50
0.5
0
0
15
2
x 10
4
x [m]
6
8
0
0
2
4
x [m]
6
High recycling ELM-free SOL
19
n [m ]
Ti Fluid
Te Fluid
Ti PIC
Te PIC
200
Fluid
PIC
-3
8
T [eV]
150
10
100
5
50
0
0
2
4
x [m]
6
8
0
0
2
4
x [m]
6
8
ELMy SOL for JET-like conditions
• PeEDGE = 2.5 MW, PiEDGE = 6.5 MW
nsepbefore ELM = 0.8 1019 m-3 (low recycling)
= 1.7 1019 m-3 (high recycling)
ce,i before ELM = 0.75 m2/s, D before ELMe = 0.10 m2/s
•
nsepELM = 5 1019 m-3 (low recycling)
= 1020 m-3 (high recycling)
Te,i ELM = 1.5 keV (low recycling)
= 0.75 keV (high recycling)
cELM/cbefore ELM = DELM/D before ELM = 100
tELM = 200 ms , DWELM ~ 100 kJ
Low recycling case
The secondary electrons (SE) do not play any significant role
2000
without SE (t=0 mks)
with SE (t=0 mks)
without SE (t=150 mks)
with SE (t=150 mks)
Potential [V]
T [eV]
800
1500
without SE (t=0 mks)
with SE (t=0 mks)
without SE (t=150 mks)
with SE (t=150 mks)
1000
e
600
1000
400
500
0
0
200
2
4
x [m]
6
8
0
0
2
Potentil and electron temperature profiles in the
SOL, as parameters most „sensitive“ to the SE.
4
x [m]
6
8
5
x 10
19
t=0 mks
t=50 mks
t=200 mks
t=250 mks
t=400 mks
n [m-3]
4
e
Potential [V]
2000
3
1500
2
1000
1
500
0
0
2
4
x [m]
6
8
t=0 mks
t=50 mks
t=200 mks
t=250 mks
t=400 mks
1000
T [eV]
e
800
t=0 mks
t=50 mks
t=200 mks
t=250 mks
t=400 mks
2500
0
0
2
4
x [m]
6
t=0 mks
t=50 mks
t=200 mks
t=250 mks
t=400 mks
1400
1200
8
T [eV]
i
1000
600
800
400
600
400
200
200
0
0
2
4 x [m]
6
8
0
0
2
4
x [m]
6
8
From fluid simulation
1.5
19
n [x2.10
T [keV]
e
T [keV]
4
-3
m ]
x 10
From PIC simulation
5
V [m/s]
||i
i
2
1
0
t=0 mks
t=50 mks
t=200 mks
t=250 mks
t=400 mks
0.5
-2
t [mks]
0
0
100
200
300
-4
0
400
2
4
x [m] 6
8
From PIC simulation
From PIC simulation
10
2500
x 10
23
F (outer divertor)
e
F (outer divertor)
i
F (inner divertor)
e
F (inner divertor)
F [1/sm 2]
Potential [V]
2000
8
1500
6
1000
4
500
i
2
t [mks]
0
0
50
100
150
t [mks]
200
0
0
50
100
150
200
From PIC simulation
El. (outer divertor)
Ions (outer divertor)
El. (inner divertor)
Ions (inner divertor)
500
q [MW/m2]
x
400
300
200
100
0
0
500
100
t [mks]
200
From fluid simulation
q MW/m
2
400
300
200
100
t [mks]
0
0
100
200
300
400
High recycling case
The secondary electrons (SE) do not play any significant role
without SE (t=0 mks)
with SE (t=0 mks)
without SE (t=130 mks)
with SE (t=130 mks)
500
400
Potential [eV]
300
without SE (t=0 mks)
with SE (t=0 mks)
without SE (t=130 mks)
with SE (t=130 mks)
350
300
T [eV]
e
250
200
200
100
150
0
100
-100
50
-200
-300
0
2
4
x [m]
6
8
0
0
2
Potential and electron temperature profiles in the
SOL, as parameters most „sensitive“ to the SE.
4
x [m]
6
8
2
x 10
21
800
t=0 mks
t=65 mks
t=130 mks
-3
n [m ]
e
t=0 mks
t=65 mks
t=130 mks
Potential [V]
600
1.5
400
1
200
0.5
0
0
0
2
4
x [m]
6
t=0 mks
t=65 mks
t=130 mks
350
300
8
T [eV]
-200
0
2
4
x [m]
6
1000
t=0 mks
t=65 mks
t=130 mks
T [eV]
i
e
8
800
250
200
600
150
400
100
200
50
0
0
2
4
x [m]
6
8
0
0
2
4
x [m] 6
8
From PIC simulation
5
x 10
4
6
V
||e
t=0 mks
t=65 mks
t=130 mks
[m/s]
3
1
2
0
1
-1
0
-2
1200
2
4
x [m]
6
8
From fluid simulation
17
-3
n [x10 m ]
Te [eV]
Ti [eV]
1000
5
From PIC simulation
V [m/s]
||i
2
3
-1
0
x 10
t=0 mks
t=65 mks
t=130 mks
-3
0
1000
2
4
x [m]
6
8
From fluid simulation
q MW/m
2
800
800
600
600
400
400
200
200
0
0
100
200
300
t [mks]
400
0
0
100
200
300
t [mks]
400
Conclusions
• Sheath effects play an extremely important role in both
the ELM-free and the ELMy SOL:
i. The electron heat flux due to the “cut-off” effect can exceed the
Spitzer-Härm heat flux even in a highly collisional regime.
ii. the potential drop in the sheath affects the time scale of heat loads
on the divertor plates during the ELM.
• The secondary electrons do not play any significant role
in the ELMy SOL
Conclusions
•
During ELM activity the time evolution of the heat load
on the divertor plates exhibits two peaks:
i. The first (small) one appears in an electron time scale after ELM
set-on and corresponds to highly energetic ELM electrons arriving
at the divertor.
ii. The second peak corresponds to the main ELM burst propagating
through the SOL with a high-energy ion speed.
•
For more realistic modelling of the ELMy SOL it is
necessary to consider the neutrals self-consistently