PIC simulations of the propagation of type-1 ELM-produced energetic particles on the SOL of JET D....
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Transcript of PIC simulations of the propagation of type-1 ELM-produced energetic particles on the SOL of JET D....
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
1Plasma and Energy Physics Group, Association Euratom – ÖAW, Department
of Theoretical Physics, University of Innsbruck, Innsbruck, Austria2EFDA, Close Support Unit Garching, Max-Planck-Institut fuer Plasmaphysik,
D-85748 Garching bei Muenchen, Germany3UKAEA Fusion, Association Euratom-UKAEA, Culham Science Center,
Abingdon, United Kingdom
*Permanent address: Institute of Physics, Georgian Academy of Sciences,
Tbilisi, Georgia
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 : 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
inksources SSAt
A
||
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 ELM, DELM ~ (10 - 1000) x 0, D0 during ELM in pedestal & SOL Experiments p@ELM ~ (1 - 2) p@between ELMs
ELM simulation for ITER with B2-Eirene [Loarte, 2000]
Pedestal only Pedestal + SOL
Te Te @ ELM
Radiation 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:
.)0,0,(
N, , 2, 1, i ,
,
x
ii
ii
ii
EE
VXdt
d
BVEm
qV
dt
d
Nonlinear Coulomb and charged-neutral particle collisions
.,0
2 xxx E
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
Elastic A + A+ - A + A+
Charge-exchange A + A+ - A+ + A A = H, D, T
Charged-neutral particle collision cross-sections
10-3
10-1
101
10310
-1
100
101
E [eV]
10-18 m2
elasticcharge exchange
100
102
10410
-2
10-1
100
101
102
E [eV]
10-20 m2
ionizationelastic collisionexcitation
Secondary electron emission is implemented in the code.
Secondary electron emission due to electron impact
./108.1,0
,/108.1,18.010/5
56
smVif
smVifsmVi
i
2,60,cos/1,/22exp 00
0 elseifEEE
Ee
For graphite ,3000 eVE
Secondary electron emission due to ion impact [Diem, 2001]
.10
0 1000 20000
0.2
0.4
0.6
0.8
1
E [eV]
e
0 400 8000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
V [km/s]
i
Particle sourceDivertor
plate
Divertor plate
x
B
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
0 1 2 3 4 5 6 7-4
-3
-2
-1
0
1
2
3
4x 10
5
qx [W/m2]
x [m]
PICSpitzer (Sp.)Sp.+sheath
Source effect
Electron heat flux profile from PIC, and corresponding Spitzer-Härm and the Spitzer-Härm + “sheath” heat fluxes. e=130.
• Sheath effects play an important role not only in the ELMy but also in the ELM-free SOL
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 charged- neutral collisionality in the PIC simulation it is necessary
to shift the neutral density (obtained from the fluid model).
0 5 10 150
2
4
6
8
10
12x 10
18
x [mm]
nN
(fluid)
ni (fluid)
ni (PIC)
nN
(PIC)
Two sets of simulations have been made for low and high recycling SOL
0 2 4 6 80
0.5
1
1.5
2
2.5
3x 1019
n [m-3]
x [m]
FluidPIC
0 2 4 6 80
50
100
150
200
250T [eV]
x [m]
Ti Fluid
Te Fluid
Ti PIC
Te PIC
Low recycling ELM-free SOL
0 2 4 6 80
5
10
15 x 1019
n [m-3]
x [m]
FluidPIC
0 2 4 6 80
50
100
150
200T [eV]
x [m]
Ti Fluid
Te Fluid
Ti PIC
Te PIC
High recycling ELM-free SOL
ELMy SOL for JET-like conditions
• PeEDGE = 2.5 MW, Pi
EDGE = 6.5 MW
nsepbefore ELM = 0.8 1019 m-3 (low recycling)
= 1.7 1019 m-3 (high recycling) e,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)
ELM/before ELM = DELM/D before ELM = 100
ELM = 200 s , WELM ~ 100 kJ
Low recycling case
The secondary electrons (SE) do not play any significant role
Potentil and electron temperature profiles in the SOL, as parameters most „sensitive“ to the SE.
0 2 4 6 80
500
1000
1500
2000Potential [V]
x [m]
without SE (t=0 mks)with SE (t=0 mks)without SE (t=150 mks)with SE (t=150 mks)
0 2 4 6 80
200
400
600
800
1000
Te [eV]
x [m]
without SE (t=0 mks)with SE (t=0 mks)without SE (t=150 mks)with SE (t=150 mks)
0 2 4 6 80
1
2
3
4
5x 1019
ne [m-3]
x [m]
t=0 mkst=50 mkst=200 mkst=250 mkst=400 mks
0 2 4 6 80
500
1000
1500
2000
2500Potential [V]
x [m]
t=0 mkst=50 mkst=200 mkst=250 mkst=400 mks
0 2 4 6 80
200
400
600
800
1000
1200
1400
Ti [eV]
x [m]
t=0 mkst=50 mkst=200 mkst=250 mkst=400 mks
0 2 4 6 80
200
400
600
800
1000T
e [eV]
x [m]
t=0 mkst=50 mkst=200 mkst=250 mkst=400 mks
0 100 200 300 4000
0.5
1
1.5From fluid simulation
t [mks]
n [x2.1019 m-3]T
e [keV]
Ti [keV]
0 50 100 150 2000
500
1000
1500
2000
2500Potential [V]
t [mks]
0 2 4 6 8-4
-2
0
2
4x 105
V||i
[m/s]
x [m]
t=0 mkst=50 mkst=200 mkst=250 mkst=400 mks
0 50 100 150 2000
2
4
6
8
10 x 1023
F [1/sm2]
t [mks]
Fe (outer divertor)
Fi (outer divertor)
Fe (inner divertor)
Fi (inner divertor)
From PIC simulation
From PIC simulation
From PIC simulation
0 100 200 300 4000
100
200
300
400
500From fluid simulation
t [mks]
q MW/m2
From PIC simulation
0 100 2000
100
200
300
400
500q
x [MW/m2]
t [mks]
El. (outer divertor)Ions (outer divertor)El. (inner divertor)Ions (inner divertor)
High recycling case
The secondary electrons (SE) do not play any significant role
0 2 4 6 8-300
-200
-100
0
100
200
300
400
500Potential [eV]
x [m]
without SE (t=0 mks)with SE (t=0 mks)without SE (t=130 mks)with SE (t=130 mks)
Potential and electron temperature profiles in the SOL, as parameters most „sensitive“ to the SE.
0 2 4 6 80
50
100
150
200
250
300
350
Te [eV]
x [m]
without SE (t=0 mks)with SE (t=0 mks)without SE (t=130 mks)with SE (t=130 mks)
0 2 4 6 80
0.5
1
1.5
2x 1021
ne [m-3]
x [m]
t=0 mkst=65 mkst=130 mks
0 2 4 6 8-200
0
200
400
600
800Potential [V]
x [m]
t=0 mkst=65 mkst=130 mks
0 2 4 6 80
50
100
150
200
250
300
350
Te [eV]
x [m]
t=0 mkst=65 mkst=130 mks
0 2 4 6 80
200
400
600
800
1000T
i [eV]
x [m]
t=0 mkst=65 mkst=130 mks
0 2 4 6 8-1
0
1
2
3
4
5x 106
V||e
[m/s]
x [m]
t=0 mkst=65 mkst=130 mks
0 2 4 6 8-3
-2
-1
0
1
2
3x 105
V||i
[m/s]
x [m]
t=0 mkst=65 mkst=130 mks
0 1000 200 300 4000
200
400
600
800
1000
1200From fluid simulation
t [mks]
n [x1017 m-3]T
e [eV]
Ti [eV]
0 100 200 300 4000
200
400
600
800
1000From fluid simulation
t [mks]
q MW/m2
From PIC simulation From PIC simulation
• 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
Conclusions