Download ETPD: The Facts and The FAQs

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 Angeles
February 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 Termination
1.
2.
Occurs at plasma/neutral gas pressure equilibrium
Plasma terminates on current-free ambipolar sheath
determined by a generalized Ohm’s law
3. Heating, ionization occur in NBL

Measured scaling laws in ETPD
Motivation: Aurora
The auroral-arc current loop associated
with a perpendicular electric field imposed
in the magnetosphere [Borovsky 1993]
Aurora over Jokulsarlon Lake, Iceland
Stephane Vetter, “Nuits sacrees” Feb. 2011
Schematic view of parallel currents j||, plasma motions,
vperp, electric fields, and potential contours above auroral
arc, sketched in green [Haerendel 1996]
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 divertor design for DIII-D
Gaseous divertor design for JET
Gaseous divertors designed to
dissipate plasma particles,
momentum, and energy on
neutral gas before touching wall
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
LaB6 source
injects primaries
to form then heat
the plasma
C.M. Cooper et al, Rev of Sci Inst. 81 083503 (2010)
R.J. Taylor et al, Nuclear Fusion 42 46-51 (2002)
ETPD Plasma
(pink) follows the
helical magnetic
field up to 120 m
Picture of a LaB6 Cathode
Frame and Shielding
Heater
Anode
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.
Neutral Boundary Layer
Probe
400 V discharge
2 mTorr
300 V discharge
2.5 mTorr
2.2 kA
220 V discharge
3.6 mTorr
Energy Balance in ETPD
220 V
e
e e
e
e
e
ee e
ee
e e
e
e
e eHEAT
e
e
Helium
Gas
B
Ionosphere
e e ee e
i
<100 kV
ii
i
ee e e e i
e
e
e e
HEAT
e e
Atmosphere
Energy Balance in Aurora
3 Zones in ETPD Plasma
+ Thermalization
Heat
of primaries
+ ionization >
Density losses
- Conduction/
- Ohmic Heating
ionization
and cooling
- Radial diffusion - Ionization and
Radial diffusion
Take Data
Energy input length
mfp, prim ~ 15m
Energy loss length
p /  r r ~ 15m
Efield Term.
 in / v p ~ 1.5m
Ambipolar Termination
Sheath in NBL!
1
0
-1
-2
-3
-4
Relative y coord (cm)
Plasma potential in neutral gas
boundary indicative of large fieldaligned electric field
40
20
0
-20
-40
-60 -40 -20 0
20 40 60
Fp (eV) Relative x coord (cm)
-40
-20
0
20
40 60
Relative x coord (cm)
-40 -20
0
20
40
-40
-20
0
20
40 60
Relative x coord (cm) Relative x coord (cm)
Neutral fill of 3.6 mTorr He, a plasma discharge of 194 A 220 V, Btor=250 G, Bver=6 G,
Generate
Radial Profiles
1
0
-1
-2
-3
-4
Relative y coord (cm)
Used to study rate at
which particles,
momentum, and heat
move across the field and
out of the plasma
40
20
0
-20
-40
-60 -40 -20 0
20 40 60
Fp (eV) Relative x coord (cm)
-40
-20
0
20
40 60
Relative x coord (cm)
-40 -20
0
20
40
-40
-20
0
20
40 60
Relative x coord (cm) Relative x coord (cm)
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 NBL
1
0
-1
-2
-3
-4
Relative y coord (cm)
A
Plot data along the
center of plasma
coordinate “s”
Three zones!
A B C
B C
40
20
0
-20
-40
-60 -40 -20 0
20 40 60
Fp (eV) Relative x coord (cm)
-40
-20
0
20
40 60
Relative x coord (cm)
-40 -20
0
20
40
-40
-20
0
20
40 60
Relative x coord (cm) Relative x coord (cm)
Neutral fill of 3.6 mTorr He, a plasma discharge of 194 A 220 V, Btor=250 G, Bver=6 G,
Neutral Boundary Layer Model
• Three-fluid, current-free
• Continuity equation: ionization and losses

n p v p,s   S p   p,
s

nnvn,s   S p   n,
s
• Momentum equation: pressure equilibration
A
• Momentum equation: generalized Ohms Law
pe
Te
eEs  
 0.71  t n n p k B
 me n p v p , s  vn , s  en
B

 p p  pn   mi v p,s p,  vn,s n,   0
s
s
s
• Heat equation: ionization and Ohmic heating
Te
3
n p v p,s k B
 en p v p , s Es  EionzS p
2
s
C
Zone A: Pressure Equilibration
For 𝑝𝑝 ≥ 𝑝𝑛
• Diffusivity argument: Neutral density convected
out along field by plasma, diffuses across field
𝐷𝑎,||
𝑘𝐵 𝑇𝑛
≫ 𝐷𝑛 =
> 𝐷𝑎,⊥
𝜈𝑛
• Drag force limited to cross-field neutral diffusion
rate
𝝂𝒅𝒓𝒂𝒈 = 𝜵⊥ 𝜞𝒏,⊥ /𝒏𝒏 ≤ 𝑫𝒏 / 𝑹𝒑 𝟐
• Axial neutral flow develops from force balance
𝟎.𝟓𝝂𝒊𝒏 −𝝂𝒄𝒙 /𝒏𝒏
𝑣𝑛,𝑠 =𝑣𝑝,𝑠
𝟎.𝟓𝝂𝒊𝒏 −𝝂𝒄𝒙 /𝒏𝒏 +𝜵⊥ 𝜞𝒏,⊥ /𝒏𝒏
Momentum gained
from plasma
Momentum lost to
stationary neutrals
Electron Temperature in Zone A
-1
Fp
• Constant Te
-2
• Ionization ~ 0
(eV)
-3
Te
(eV)
3
Te
Te  2.2 eV
2
2400
2600
2800
3000
3200
Distance from anode (cm)
mi

en ~ 100 m
me
Plasma Velocity in Zone A
-1
Fp
• Plasma velocity is
flat
• Momentum balance
-2
(eV)
-3
vp
2
vcr , s  2 105 cm/s
0.5
  p , ~ Da ,
0.4
  n, ~ Dn,a
0.3
(105cm/s)
Plasma mach at 2.2 eV
4
0.2
0.1
0
2400
2600
2800
3000
Distance from anode (cm)
0
3200
pe
  mi v p , s  r p ,r 
s
 mi ne v p , s vn , s 0.5 in  cx 
• Sets a critical
velocity
veq , s cs
  p , 
  p ,    n ,
Plasma Density in Zone A
-1
Fp
• Plasma density is
dropping from radial
losses
-2
(eV)
-3
v p,s
1.2
n p
s
  r p ,r   Dr
Da , 
ne
0.8
(1012/cm3)
0.4
2400
Dr
DBohm
2600
2800
3000
3200
Distance from anode (cm)
1
Dr ~ 4 Da , ~ DBohm
2
 ~ 10 cm
np
 2
Zone B: Ambipolar Electric Field
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.
Potential Structure in NBL
• Plasma isopotentials form
“nested V’s”
• White arrows
show electric field,
parallel field 10x
ei
• Quasineutral
Colormap of plasma potential from 1,300
points interpolated onto toroidal coordinates
en
D
Electron Temperature in Zone B
-1
Fp
-2
(eV)
-3
Te
(eV)
3
Fp
• Electron
temperature rises
with potential
• For
me
en  LF 
en
mi
Te ~F p ~1 eV
2
2400
2600
2800
3000
3200
Distance from anode (cm)
Plasma Velocity in Zone B
-1
Fp
• Plasma velocity
drops due to drag on
neutrals
-2
(eV)
-3
4
Plasma mach at 2.2 eV
vp
0.5
0.4
0.3
2
(105cm/s)
0.2
0.1
0
2400
2600
2800
3000
Distance from anode (cm)
0
3200
The difference between momentum
and temperature loss
Electrons
• Momentum loss:
 en – faster
• Energy loss:
me
 en – slower
Ions
• Momentum loss:
.5 in cx – slower
• Energy loss:
.5 in cx– faster
In electric field,
In electric field, ions
mi
electrons
Plasma Density in Zone B
-1
Fp
• Plasma density is
dropping from radial
losses
-2
(eV)
-3
• Balance between
Flux conservation
1.2
ne
 v p,s   n p
0.8
Adiabatic heating
(1012/cm3)
 Te   n p
0.4
2400
2600
2800
3000
3200
Distance from anode (cm)
Plasma Termination
Use generalized Ohms law to solve for electric field
 eE
0
pe
Te
0
 en p E  (0.71  t n )n p
 me n p v p , s en
s
s
E
E
me v p ,s en
Je
0.19e
 en

~ 2V / m
 Ji
 en
for tn  0.1
, J tot  0
Zone C: Additional Ionization
Te 2.2eV
R. K. Janev, Elementary Processes in Hydrogen and Helium Plasmas (1987)
Electron Temperature in Zone C
-1
Fp
• Prediction: Electron
temperature
continues to rise
rapidly with potential
-2
(eV)
-3
Te
(eV)
3
2
2400
2600
2800
3000
3200
Distance from anode (cm)
Electron Temperature in Zone C
-1
Fp
-2
F p ~ 2.5eV
(eV)
-3
Te
(eV)
3
v|4.7 eV
~1000
v|2.2 eV
2
2400
2600
2800
3000
3200
Distance from anode (cm)
Plasma Density in Zone C
-1
Fp
• Prediction: Plasma
density continues to
drop
-2
(eV)
-3
1.2
ne
0.8
(1012/cm3)
0.4
2400
2600
2800
3000
3200
Distance from anode (cm)
Plasma Density in Zone C
-1
Fp
-2
(eV)
-3
1.2
ne
0.8
10%
(1012/cm3)
0.4
2400
2600
2800
3000
3200
Distance from anode (cm)
Plasma Production in Boundary
If all energy gained went into plasma production
how much could you make? For Tb  Ta , vb  va
QF  Qionz
ne
F
2.5eV


~ 10%
ne
 ionz  Te 24.6eV  2.2eV
What’s the mean free path of ionization?
v pz
nn v|4.7 eV
~ 10 cm
Any energy gained by electric field is quickly
absorbed by ionization
Plasma Velocity in Zone C
-1
Fp
• Prediction: Plasma
velocity will drop to 0
-2
(eV)
-3
4
Plasma mach at 2.2 eV
vp
0.5
0.4
0.3
2
(105cm/s)
0.2
0.1
0
2400
2600
2800
3000
Distance from anode (cm)
0
3200
Plasma Velocity in Zone C
-1
Fp
-2
(eV)
-3
4
Plasma mach at 2.2 eV
vp
0.5
0.4
0.3
2
(105cm/s)
0.2
0.1
0
2400
2600
2800
3000
Distance from anode (cm)
0
3200
• Additional flux is
generated by the
ionization at the end
of the plasma
• Still slowing down
after ionization ends
NBL Conserved Quatities
Axial Plasma Flux:
4
1.4
p,s=npvp,s
Pp=(np(Ti+Te)/(nnTn))
Normalized Plasma Pressure:
1.0
0.6
2400
2600 2800 3000 3200
Distance from anode (cm)
Normalized Plasma Pressure:
• End of the plasma occurs where
pp=pn
• Dropping pressure “interrupted”
by termination E field
2
0
2400
2600 2800 3000 3200
Distance 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)
Scaling of Ambipolar Electric Field
The potential
marks a
“footprint”
for the
boundary of
the plasma
49 kW
43 kW
39 kW
The location and
magnitude of Electric
field terminating the
plasma change as a
function of input
power
Measure plasma
parameters
Scaled Plasma Parameters pre-NBL
(a)
• Te is flat at 2.2 eV
(b)
• Extra power raises
density
• Axial flow drops
(c)
Scaling Study
pp=pn
seq,m=seq,t
Es,m=Es,t
Measured electric field, Es,m,
scales like the theoretical
ambipolar value
E s ,t  
me v p , s en
0.19e
Measured termination point,
seq,m, coincides with location of
pressure equilibration
seq ,t 
v p ,s R p2
Dr
 (Te  Ti )n p (s0 ) 

ln 
Tn nn


Modified Ambipolar Flow in ETPD
Electron current
Ion current
Electron current
Ion current
Electron current
Ion 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
J T ,meas    Bmeas
•Drift speed associated
with current << bulk flow
0.9 𝑣𝑒,𝑠 < 𝑣𝑖,𝑠 < 𝑣𝑒,𝑠
Types of Current
Note: Steady
state so Jpolz = 0
Some currents diverge and need to
be closed to maintain J=0
Non Transport
Causing
Some
currents
are
associated
with
particle
drifts and
transport
Transport
Causing
Divergence-Free
• Poloidal Hall (i-n)
Current (+)
• Poloidal
Diamagnetic
Current (-)
Non Divergence-Free
• Parallel (e-n) Current
• Radial Pederson (i-n)
Current
• Vertical/B Currents
Estimation of Jr
Jr
• Axial current tied
to Radial current
JS
Ar
JSo+DS = JSo + Jr
AS
Kirchoff’s Junction Rule
 r pr
E  Er 
 mi vir in
ne
*
r
J ir   in, Er*
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 Simulation
Measured 5 things: ne , Te , vi ,  p , J p
Model neutral gas
Solve 5 equations + neutral gas transport:
vez
ne
ne
 vez
 S en
z
z
vez
ne
Te

ne vez
 Te

 ne
  ev
z
z
z
z
viz
ne
ne
 viz
 S in
z
z
viz
ne

ne viz
 Ti
 ne
  iv
z
z
z
Te
qe
vez
3
ne vez

 neTe
 S eT
2
z
z
z
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!