View
224
Download
0
Category
Preview:
Citation preview
Transport in a field aligned magnetized plasma and neutral gas boundary:
The end of the plasma…C.M. Cooper, W. Gekelman, P. Pribyl, J. Maggs, Z. Lucky
University of California, Los AngelesFebruary 15, 2013
Overview• Motivation– Relation to Auroral Physics, Divertor Physics
• Summary of Enormous Toroidal Plasma Device– Model of ETPD plasma regions
• Neutral Boundary Layer model: Plasma Termination1. Occurs at plasma/neutral gas pressure equilibrium 2. Plasma terminates on current-free ambipolar sheath
determined by a generalized Ohm’s law3. Heating, ionization occur in NBL
Measured scaling laws in ETPD
Motivation: Aurora
Schematic view of parallel currents j||, plasma motions, vperp, electric fields, and potential contours above auroral
arc, sketched in green [Haerendel 1996]
Aurora over Jokulsarlon Lake, IcelandStephane Vetter, “Nuits sacrees” Feb. 2011
The auroral-arc current loop associated with a perpendicular electric field imposed
in the magnetosphere [Borovsky 1993]
J. Borovsky, J. Geo Res 98, A4 6101-6138 (1993)G. Haerendel, J. Atmos. Terr. Phys. 58, 1-4 71-83 (1996)
Motivation: Gaseous Divertors
Gaseous divertors designed to dissipate plasma particles, momentum, and energy on neutral gas before touching wallGaseous divertor design for JET
Gaseous divertor design for DIII-D
R. W. Conn, Fusion and Eng. Design 14 81-97 (1991)
Diagram of the ETPD
Toroidal Magnets (red) provide a 250 G confining field
Vertical Magnets (blue) provide a 6 G vertical field to space out rings
ETPD Plasma (pink) follows the helical magnetic field up to 120 m
LaB6 source injects primaries to form then heat the plasma
R.J. Taylor et al, Nuclear Fusion 42 46-51 (2002)C.M. Cooper et al, Rev of Sci Inst. 81 083503 (2010)
Frame and Shielding
Heater
CathodeAnode
Picture of a LaB6 Cathode
Experimental Setup• Primary electrons boiled off LaB6 are accelerated along the field by anode.
• Primaries ionize neutral gas to create and heat plasma.
• Data taken where plasma ends, 90% around machine.
Probe
400 V discharge2 mTorr
300 V discharge2.5 mTorr
220 V discharge3.6 mTorr
Neutral Boundary Layer
2.2 kA
Energy Balance in ETPDe
ee
e ee e e e
e eeee
e ee ei
e
iiii
e ee ee
e
ee e
ee H
EAT
HEAT
HEA
T
HEAT
HEA
T
HEAT
HEA
T
HEAT
HEA
T
HEAT
HEA
T
HEAT
220 V
<100 kV
B
Energy Balance in Aurora
Atmo-sphere
Ionosphere
HEAT
HeliumGase
e ee
eHEAT
3 Zones in ETPD Plasma
Heat
Density
- Conduction/ ionization- Radial diffusion
Energy loss length Efield Term.Energy input length
+ Thermalization of primaries+ ionization > losses
mprimmfp 15~, mrrp 15~/ mvpin 5.1~/
- Ohmic Heating and cooling- Ionization and Radial diffusion
Take Data
Ambipolar Termination Sheath in NBL!
Plasma potential in neutral gas boundary indicative of large field-
aligned electric field
Neutral fill of 3.6 mTorr He, a plasma discharge of 194 A 220 V, Btor=250 G, Bver=6 G,
Relative x coord (cm) Relative x coord (cm) Relative x coord (cm) Relative x coord (cm)
Rela
tive
y co
ord
(cm
)
Fp (eV)-40 -20 0 20 40 60-60 -40 -20 0 20 40 60 -40 -20 0 20 40 -40 -20 0 20 40 60
40
20
0
-20
-40
1
0
-1
-2
-3
-4
GenerateRadial Profiles
Neutral fill of 3.6 mTorr He, a plasma discharge of 194 A 220 V, Btor=250 G, Bver=6 G,
Relative x coord (cm) Relative x coord (cm) Relative x coord (cm) Relative x coord (cm)
Rela
tive
y co
ord
(cm
)
Fp (eV)-40 -20 0 20 40 60-60 -40 -20 0 20 40 60 -40 -20 0 20 40 -40 -20 0 20 40 60
40
20
0
-20
-40
1
0
-1
-2
-3
-4
Used to study rate at which particles, momentum, and heat move across the field and out of the plasma
Neutral fill of 3.6 mTorr He, a plasma discharge of 194 A 220 V, Btor=250 G, Bver=6 G,
Generate Axial Profiles in NBLPlot data along the center of plasma coordinate “s” Three zones! A B C
Relative x coord (cm) Relative x coord (cm) Relative x coord (cm) Relative x coord (cm)
Rela
tive
y co
ord
(cm
)
Fp (eV)-40 -20 0 20 40 60-60 -40 -20 0 20 40 60 -40 -20 0 20 40 -40 -20 0 20 40 60
40
20
0
-20
-40
1
0
-1
-2
-3
-4
A B C
Neutral Boundary Layer Model• Three-fluid, current-free
,, ppspp Svns
ensnsppee
Bpne
s vvnms
Tknt
s
peE ,,71.0
pionzssppe
Bspp SEEvens
Tkvn
,,2
3
• Momentum equation: pressure equilibration
• Heat equation: ionization and Ohmic heating
• Momentum equation: generalized Ohms Law
• Continuity equation: ionization and losses
0,,,,
nsnpspinp vvmpps
,, npsnn Svns A
B
C
Zone A: Pressure Equilibration
• Diffusivity argument: Neutral density convected out along field by plasma, diffuses across field
𝐷𝑎,∨¿≫𝐷𝑛=𝑘𝐵𝑇 𝑛
𝜈𝑛
>𝐷𝑎 ,⊥
/
=Momentum gained from plasmaMomentum lost to stationary neutrals
𝑝𝑝≥𝑝𝑛For
• Drag force limited to cross-field neutral diffusion rate
• Axial neutral flow develops from force balance
Electron Temperature in Zone A
• Constant
• Ionization ~ 0
mm
men
e
iTe 001~
eVTe 2.2
eT
2400 2600 2800 3000 3200Distance from anode (cm)
-1
-2
-3(eV)
Fp
3
2(eV)
Te
0.5
0.4
0.3
0.2
0.1
0
Plasma m
ach at 2.2 eV
Plasma Velocity in Zone A
• Plasma velocity is flat• Momentum balance
• Sets a critical velocity
,,
,,
np
psseq cv
cxinsnspei vvnm 5.0,,
ann
ap
scr
D
D
scmv
,,
,,
5,
~
~
/102
rprspie vms
p,,
2400 2600 2800 3000 3200Distance from anode (cm)
-1
-2
-3(eV)
Fp
4
2
0
(105cm/s)
vp
Plasma Density in Zone A
• Plasma density is dropping from radial losses
cm
DDD Bohmar
10~2
1~4~ ,
2,,
p
rrprp
sp
nD
s
nv
2400 2600 2800 3000 3200Distance from anode (cm)
-1
-2
-3(eV)
Fp
1.2
0.8
0.4(1012/cm3)
nerD
,aD
BohmD
ee
e
i
i
e
eie i i i
i
iei
e
iei
ee
iei
e
ii
e
ei e i e
i
Current-free plasma sees neutral gas at end
Electrons stop, ion current penetrates
Electric field develops, drives electron current
Electric field maintains Current free term.
Zone B: Ambipolar Electric Field
Potential Structure in NBL
lei
len
lDColormap of plasma potential from 1,300 points interpolated onto toroidal coordinates
• Plasma iso-potentials form “nested V’s”
• White arrows show electric field, parallel field 10x
• Quasineutral
Electron Temperature in Zone B
• Electron temperature rises with potential• For
eVT pe 1~~
eni
een m
mL
2400 2600 2800 3000 3200Distance from anode (cm)
-1
-2
-3(eV)
Fp
3
2(eV)
Te
Fp
0.5
0.4
0.3
0.2
0.1
0
Plasma m
ach at 2.2 eV
Plasma Velocity in Zone B
• Plasma velocity drops due to drag on neutrals
2400 2600 2800 3000 3200Distance from anode (cm)
-1
-2
-3(eV)
Fp
4
2
0
(105cm/s)
vp
The difference between momentum and temperature loss
Electrons• Momentum loss: – faster• Energy loss: – slower
In electric field,
electrons HEAT.
en
eni
e
m
m
cxin 5.
Ions• Momentum loss: – slower• Energy loss: – faster
In electric field, ions SLOW.
cxin .5
Plasma Density in Zone B
• Plasma density is dropping from radial losses
• Balance between Flux conservation
Adiabatic heatingpsp nv ,
pe nT
2400 2600 2800 3000 3200Distance from anode (cm)
-1
-2
-3(eV)
Fp
1.2
0.8
0.4(1012/cm3)
ne
Plasma Termination
Use generalized Ohms law to solve for electric field
ensppee
pnpe vnm
s
TntEen
s
p ,)71.0(0
mVe
vmE enspe /2~
19.0,
0 eE
1.0ntfor
0,
toten
i
en
e JJJ
E
Zone C: Additional Ionization
eVTe 2.2
R. K. Janev, Elementary Processes in Hydrogen and Helium Plasmas (1987)
Electron Temperature in Zone C
• Prediction: Electron temperature continues to rise rapidly with potential
2400 2600 2800 3000 3200Distance from anode (cm)
-1
-2
-3(eV)
Fp
3
2(eV)
Te
Electron Temperature in Zone C
eVp 5.2~
1000~|
|
2.2
7.4
eV
eV
v
v
IONIZATION
2400 2600 2800 3000 3200Distance from anode (cm)
-1
-2
-3(eV)
Fp
3
2(eV)
Te
Plasma Density in Zone C
• Prediction: Plasma density continues to drop
2400 2600 2800 3000 3200Distance from anode (cm)
-1
-2
-3(eV)
Fp
1.2
0.8
0.4(1012/cm3)
ne
Plasma Density in Zone C
IONIZATION
2400 2600 2800 3000 3200Distance from anode (cm)
-1
-2
-3(eV)
Fp
1.2
0.8
0.4(1012/cm3)
ne
10%
Plasma Production in BoundaryIf all energy gained went into plasma production
how much could you make? For
What’s the mean free path of ionization?
Any energy gained by electric field is quickly absorbed by ionization
abab vvTT ,
ionzQQ
%10~2.26.24
5.2
eVeV
eV
Tn
n
eionze
e
cmvn
v
eVn
pz 10~| 7.4
0.5
0.4
0.3
0.2
0.1
0
Plasma m
ach at 2.2 eV
Plasma Velocity in Zone C
• Prediction: Plasma velocity will drop to 0
2400 2600 2800 3000 3200Distance from anode (cm)
-1
-2
-3(eV)
Fp
4
2
0
(105cm/s)
vp
Plasma Velocity in Zone C
• Additional flux is generated by the ionization at the end of the plasma• Still slowing down after ionization ends
IONIZATION
0.5
0.4
0.3
0.2
0.1
0
Plasma m
ach at 2.2 eV
2400 2600 2800 3000 3200Distance from anode (cm)
-1
-2
-3(eV)
Fp
4
2
0
(105cm/s)
vp
NBL Conserved QuatitiesAxial Plasma Flux:
2400 2600 2800 3000 3200Distance from anode (cm)
Normalized Plasma Pressure:• End of the plasma occurs where pp=pn
• Dropping pressure “interrupted” by termination E field
2400 2600 2800 3000 3200Distance from anode (cm)
Plasma flux:• Measure of axial particle flux• Only loss of axial flux is radial flux• Filling in of profile• Kinetic effects (trapped particles)
1.4
1.0
0.6
P p=(n
p(Ti+
T e)/(n
nTn)) 4
2
0
Gp,
s=n pv
p,s
Normalized Plasma Pressure:
49 kW
43 kW
39 kW
Scaling of Ambipolar Electric Field
The location and magnitude of Electric field terminating the plasma change as a function of input power
The potential marks a “footprint” for the boundary of the plasma
Measure plasmaparameters
Scaled Plasma Parameters pre-NBL
• Axial flow drops
• Extra power raises density
• Te is flat at 2.2 eV(a)
(b)
(c)
Scaling Study
e
vmE enspe
ts 19.0,
,
nn
pie
r
pspteq nT
snTT
D
Rvs
)()(ln 0
2,
,
Measured electric field, Es,m, scales like the theoretical ambipolar value
Measured termination point, seq,m, coincides with location of pressure equilibration
Es,m=Es,t
seq,m=seq,t
pp=pn
Modified Ambipolar Flow in ETPD
Ion current
Electron current
Ion currentIon current
Electron current
Electron current
Ambipolar Flow in NBL
• Magnetic field data from probe indicates axial current
• Negative current carried by electrons moving in positive direction
Data taken at s = 2870 cm, halfway through NBL
Non-Zero Current in NBL
•NBL not current free
•Current trends to zero
•Drift speed associated with current << bulk flow
measmeasT BJ ,
0.9𝑣𝑒 , 𝑠<𝑣𝑖 ,𝑠<𝑣𝑒 , 𝑠
Types of Current
Non Divergence-FreeDivergence-FreeTr
ansp
ort
Caus
ing
Non
Tra
nspo
rt
Caus
ing
Some currents diverge and need to be closed to maintain J=0
Some currents
are associated
with particle
drifts and transport
• Poloidal Diamagnetic Current (-)
• Poloidal Hall (i-n) Current (+)
• Parallel (e-n) Current• Radial Pederson (i-n) Current• Vertical/B Currents
Note: Steadystate so Jpolz = 0
Estimation of Jr
• Axial current tied to Radial current
Jr
JS
ArJSo+DS = JSo + JrAS
Kirchoff’s Junction Rule
inirie
rrrr vm
n
pEE
*
*, rinir EJ
Future Work on NBL
• Observational– Measure plasma potential and flows in Aurora
• Experimental– Study NBL for different pressures and/or gases
• Simulation– Model in DEGAS (neutral gas collisional code)*– Model in UEDGE (transport code)*– Runge Kutta solver for fluid model**
Future work: 1.5-D SimulationMeasured 5 things: Model neutral gasSolve 5 equations + neutral gas transport:
ppiee JvTn ,,,,
ene
ezez
e Sz
nv
z
vn
ine
iziz
e Sz
nv
z
vn
eveee
eez
eze zn
z
T
z
nT
z
vvn
eTez
eeee
eze Sz
vTn
z
q
z
Tvn
2
3
ivee
iiz
ize zn
z
nT
z
vvn
Generalized Source/Sink calibrated by data
Conclusions–Plasma terminates on ambipolar electric field– Electric field occurs where diminishing plasma
pressure and neutral pressure equilibrate–NBL dominated by termination field through
Ohmic heating and ionization–NBL has a small modified ambipolar diffusion
due to differences in directional particle motilities
Thanks!
Recommended