centrifugal confinement for fusion and the maryland
TRANSCRIPT
Centrifugal Confinement for Fusion
and the Maryland Experiment (MCX)
R. F. Ellis, A. B. Hassam
A. Case, D. Gupta, Y. Huang, J. Rodgers, C. Romero-Talamas, C. Teodorescu,
A. DeSilva, R. Elton, H. Griem, P. Guzdar, R. Clary, S. Choi, R. Lunsford,
A. S. Messer, R. Reid, G. Swan, I. Uzun-Kaymak, W. C. Young
University of Maryland, College Park
PPPL 2017
Basic Idea
• centrifugal forces => axial confinement
• rotation shear => stability to interchanges
Hassam, AB, Comments Plasma Phys Cont. Fus., 18, 263, 1997
Ellis, RF; Hassam, AB; Messer, S; et al. PHYSICS OF PLASMAS 8, 2057, 2001
Previous Experiments
• IXION (LosAlamos) Boyer, et al ‘58
- mirror geometry
- ExB rotation as expected ~ 40 km/s
- impurity influx terminates discharge
• F-X (Stockholm) Lehnert, et al ‘60’s
- dipole geometry
- plasma dielectric as expected
- V0 < 10 keV limitation, arcing @ insulator
• PSP (Novosibiirsk) Volosov, et al ‘70’s
- biased, concentric ring electrodes => high V0
- high T, n < 1018
Next few slides: Ms > 1
• Mach number, Ms, is the Figure of Merit
for Equilibrium, Stability, and Lawson Breakeven.
Ms > 1
MHD Centrifugal Force Balance
=> need high Mach number
B. p = - B.[nm u. u]
p : nmu2
1 : u2/cs2 = Ms
2
“gravitational” scale height ~ 1/Ms2
=> Ms > 1
V’ can stabilize interchanges
V’ > int [ln R]1/2
Hassam, Phys Fluids B, 4, 485 1992
for smooth profiles, sonic interchanges
=> Ms > 1
Simple mirrors are unstable to
flute interchanges
•)
NMCX - 3-D Numerical Simulation
V’ shear stabilizes interchanges - flutes appear if V’ artificially supressed
Huang,Y-M, Hassam AB, Physics of Plasmas 11 (5), 2459, 2004
TRANSPORT
• Cross field, classical?
• Along B:
- Ions centrifugally confined
- energetic electrons transfer heat
- deep potential well, e/T ~ Ms2
- large Pastukhov factor
e ~ ee-1 [Ms
2/4] exp[Ms2/4]
Ms > 5 => Lawson Condition
T. M. Antonsen, private communication
A. B. Hassam, Comments Plasma Phys. Control. Fusion 18, 275, 1997
MCX Objectives
#1 Supersonic Rotation?
#2 MHD Stable?
#3 Centrifugally confined?
Goal #1:
Supersonic? yes
MCX Rm ~ 9 (Bmid = 0.2 - 0.3 T)
Hydrogen, P0 = 5-10 mtorr
ni ~ few 1020 m-3 (fully
ionized)
Ti ~ 20 – 50 eV
VBank 5-20 kV, pulse 1-10 ms
vrot uExB ~ 100 km/s
Messer, Case, Ellis, Gupta, Hassam, Lunsford,
Ghosh, Elton, Griem, APS 2003
MCX plasma parameters quasi-steady
for 1000’s of MHD instability times
MHD m
Goal#1: Doppler shifts show supersonic ExB
rotation, in red and blue shifts (up and down)
C IV Spectra
Unshifted line
Ghosh, J; Elton, RC; Griem, HR; et al. Phys Plasmas 13, 022503, 2006
c_s ~ 60 km/s
Ghosh, J; Elton, RC; Griem, HR; et al. Phys Plasmas 13, 022503, 2006
Goal #2:
MHD Stable? indirect
• MHD instability growth time MHD ~ 2 - 20s
• Measured momentum confinement time mom ~ 200-800s
• No “major disruptions” => MHD Stable?
mom MHD
ms
Voltage across plasma remains steady for
1000’s of MHD instability times
• Flow profiles
independent of charge,
consistent with EB drift
From C. Teodorescu, 2006 ICC Workshop, Austin, TX
• Stability threshold
exceeded
V’ shear is large enough to stabilize interchange modes
HFB2D B2DB2D
Comparison of fluctuations
observations and simulations
t(s)
qxp/8
OBSERVATIONS
qxp/8
qxp/8
SIMULATIONS WITH F=0 SIMULATIONS WITH F=-2
• Simulation without imposed azimuthal flow (F=0) shows “bloby” structures with no
clear
direction of propagation
• Simulations with flow (F=-2) shows propagation features similar to observations.
Uzun-Kaymak, et al, Physics of Plasmas 15, 112308 (2008)
FD2DFD2D m
t(s)
m
Fluctuations azimuthal modes versus time
OBSERVATIONS SIMULATIONS WITH F=-2
•azimuthal mode number spectrum versus time shows intermittent
excitation and stabilization of low modes numbers
• dominant difference between simulations and observations is strong
m=1 mode and more remnants of higher modes in simulations
Goal #3:
Centrifugal Confinement?
MCX diagnostics
spectrometer
Fiber optic cables
Spectrometer
with
ICCD camera
r z LGFS
5-chord visible spectrometer
visible
IR
MCX
chamber
lasers
Bragg cells
IR
visible
detectors
2 Mach-Zehnder heterodyne interferometers with IR lasers
placed at midplane and off-midplane
• Voltage divider (core - ground)
• Rogowski coil (on core)
• 3-D and 1-D magnetic probes
• External diamagnetic loops
• Multi-chord spectrometer
• IR and visible interferometers
• H detectors
HV feed-through
Midplane and axially off-midplane interferometers
2
1
2
1
r l
• Location of interferometer laser
beams through plasma:
Midplane: z2=0; r2=15 cm
Off-midplane: z1=85 cm; r1=6 cm
Teodorescu, et al, Phys. Rev. Lett. 105, 085003 (2010)
Plasma density and diamagnetic flux
are large at the magnetic minimum
DML2
DML1 2
1
n2/n1=12
DML2
DML1
2
1
n2/n1=0.4
Density changes both at midplane and off-midplane with Rm
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
1 2 3 4 5 6 7 8 9
Rm
de
ns
ity
(x
10
20 m
-3)
midplane
off-midplane
• Values at t=2 ms averaged over one momentum confinement time (=100 s).
• Fixed applied parameters except for Rm=B(z=130)/B(z=0).
Density ratio and diamagnetic flux ratio flip
when r1= r2, consistent with radial stratification
• Average values over 100 s (one
momentum confinement time) at
t=2 ms in the discharge.
r2
r1DML
r1 r2
r1DML
r1
Mirror Ratio: 2
Spectroscopic measurements of plasma rotation and ion
temperature profiles yield information on sonic Mach number
0
20
40
60
80
100
120
140
0 5 10 15 20 25 30
radial location (cm)
u (
km
/s)
0
10
20
30
40
50
0 5 10 15 20 25 30
radial location (cm)
Ti (
eV
)
0
0.5
1
1.5
2
2.5
3
0 5 10 15 20 25 30
radial location (cm)
Ms
• Line observed: C2+ of 4647.42 Å
• Measured at t=2 ms in the discharge.
0
5
10
15
20
25
30
35
40
45
50
0 2 4 6 8 10 12 14 16 18
radial location (cm)
Ti (
eV
)• Off-midplane Ti
is comparable to
Ti at midplane.
Theory fits the trend of measured data
• Measured Ms profiles available
only for Rm=8.
• Chord-averaged measurements
of Ms were made for Rm<8.
• Average of a constructed parabolic
Ms profile was matched to measurement.
1
1.25
1.5
1.75
2
2.25
1 2 3 4 5 6 7 8 9
Rm
Peak c
on
str
ucte
d M
s
DMLs
•External Magnetic Diagnostics: 7 DMLs, 8 Br loops in z-array,
and 16 Br loops in azimuthal array (movable along z). Rm=7
Magnetic Loop Layout
W.C. Young, et al Physics of Plasmas 18, 112505 (2011)
Magnetic Loop Layout
Field lines above are for mirror ratio 3. Minima occur close to outermost DMLs
Theory vs. Data – Mirror Ratio 7
• Peak rotation velocity: 110 km/s
• MA=0.4, MS=2 (for blue curves) or MS=2.5 (for green curve)
Theory vs. Data – Mirror Ratio 3
• Density and rotation velocity based on off-midplane measurements.
• Peak rotation velocity ~70 km/s
• Peak MS ~ 1.6, MA~0.5
Theory vs. Data – Fitting
• The model can be iterated, and various parameters fit to the data using a least
means square approach.
•Above is an example where the temperature and rotation velocity were fit for the
mirror ratio 7 case, minimizing error of DML measurements and interferometer ratios.
This gave a peak temperature of 21 eV, and a peak rotation velocity of 125 km/s.
The interferometer ratio is 14 vs. measured 5.
Centrifugal Confinement (CC)
• Blue and green curves are the same baseline curves as before.
• Red curves have the CC exponential factor removed from the density (set to 1).
• Similar magnitudes are due to density constraints from interferometer measurements.
• B/B ~ B~1/B. But B(z=65)/B(z=8)~1.4, while DML(8)/DML(65)~4
• Without CC term, the profiles match the profile of the vacuum field. This disagrees
with the sharp peak of DML data, and the relative size of the two bumps in BR data.
SUMMARY - for the fast (MHD) time scale
• Supersonic Flows, sheared flows, exceeding stabilization criterion
• “Quiescent”, no disruptions, steady state
• Centrifugal axial confinement, loss-cone capped, midplane to mirror density
drops
• Neutral dominated
UNANSWERED QUESTIONS
• How large, compared to classical, is the residual transport?
Is it interchange modes, or other?
• Is there a speed barrier (CIV)? Can it be exceeded?
• Insulators at fusion conditions. > 10 MV/m?
• Run without core?
• Opportunity: High-Tc High-B magnets
References (partial list)
1) Sub-Alfvenic velocity limits in magnetohydrodynamic rotating plasmas. Physics of Plasmas 17 052503 (2010)
C. Teodorescu, R. Clary, R. F. Ellis, A.B. Hassam, C. A. Romero-Talamas and W.C. Young.
2) Low Dimensional Model for the Fluctuations observed in the Maryland Centrifugal Excperiment. International Symposium of
Waves, Coherent Structures and Turbulence in Plasmas, 2010 American Institute of Physics 978-0-7354-0865-4/10
P.N.Guzdar, I. Uzun-Kaymak, A.B.Hassam, C. Teodorescu, R.F. Ellis, R.Clary, C.Romero-Talamas, and W. Young
3) Isorotation and differential rotation in a magnetic mirror with imposed ExB rotation. Physics of Plasmas 19, 072501 (2012).
C.A. Romero-Talamas, R.C. Elton, W.C. Young, R. Reid and R.F. Ellis.
4) Experimental study on the velocity limits of magnetized rotating plasmas. Physics of Plasmas 15 042504 (2008). C.
Teodorescu, R. Clary, R.F. Ellis, A.B. Hassam, R. Lunsford
5) Diamagnetism of rotating plasma. W.C. Young, A.B. Hassam, C.A. Romero-Talamas, R.F.Ellis and C. Teodorescu.
Physics of Plasmas 18, 112505 (2011)
6) Analysis and modeling of edge fluctuations and transport mechanism in the Maryland Centrifugal Experiment. I.U.Uzun-
Kaymak, P.N. Guzdar, R. Clary, R.F.Ellis, A.B. Hassam and C. Teodorescu. Physics of Plasmas 15, 112308 (2008)
7) 100 eV electron temperatures in the Maryland centrifugal experiment observed using electron Bernstein emission. R.R. Reid,
C.A. Romero-Talamas, W.C.Young, R.F.Ellis, and A.B.Hassam. Physics of Plasmas 21, 063305 (2014)
8) Confinement of Plasma along Shaped Open Magnetic Fields from the Centrifugal Force of Supersonic Plasma Rotation. C.
Teodorescu, W.C.Young, G.W. Swan, R.F.Ellis, A.B.Hassam, and C.A.ROmero-Talamas. Phys. Rev. Lett. 105, 085003 (2010)
9) Charge and mass considerations for plasma velocity measurements in rotating plasmas. C.A. Romero-Talamas, R.C.Elton, W.C.
Young, R. Reid, R.F.Ellis, A.B. Hassam. Journal of Fusion Energy, 29, 6, 543-547 (2010)
Extras
Magnetic probes could yield info
on wobbles at the edge
p + BB/0 0 p ~ p’ r r/a ~ BB/0p => r < 1 cm
There is a speed barrier at VA as expected,
but also another non-MHD barrier
40
60
80
100
120
140
160
40 80 120 160 200 240 280 320
Alfven velocity (km/s)
rota
tion
ve
locity (
km
/s)
• Consistent with “Critical Ionization Velocity” observed earlier
MA 1 in all 142 distinct data points
Rotation velocity measured
at maximum Vp.
Average values:
1/ 2( )
150 μs
p
A
i i
Vu
aB
BV
m n
Insulator long path length, clean after ~10 years
Lithium
Larger cross section
Flare out the fields at the ends
Stellarator – Mirror
Ellis, Gupta, Hassam, J. Rodgers, Teodorescu
CIV spectroscopy shows supersonic
rotation in red and blue shifts
Bottom
mcx030519-24
mcx030519-23
mcx030519-26
Top
mcx030519-16
mcx030519-17
mcx030519-18
Confirmation of
crossfield MHD dielectric constant
0
0.5
1
1.5
2
2.5
3
0 20 40 60 80 100
ne (1019
m-3
)
Cp (
10
-4 F
)
0
20
40
60
80
100
nm
ode
l (1
019 m
-3)
Teodorescu et al (PoP)
= nMc2/B2
interferometer
Q/V
momentum ~ 200-600 s
=> N 1017 m-3
Calculated timescales for comparison to MCX
discharge duration (> 5 ms) and momentum
confinement time( 200 s)
Axial Alfven time ~ LP/vA
5s
Period of rotation ~ (2pR/u)
10s
Interchange growth time ~ [(aPLP)/(T/Mp)]1/2
10s
Axial electron heat conduction time ~ (LP/)2 e
30s
Axial sonic time ~ LP/(T/Mp)1/2
30s
Electron-ion heat exchange time ~ (Mp/me)e
40s
Classical viscous damping time ~ (aP/)2 ii
8000s
( n = 2x1020 m-3, T = 30 eV, B = 0.2 T)
Charge exchange time ~ 500 s
OPERATION AT FUSION
PARAMETERS
This is an old slide; I would have to check the assumptions that went into it. Definitely includes parallel Pastukov electron losses (enhanced by Ms). Probably a mirror ratio of 10-12 is assumed. “Q” is the factor by which n*tau at T=10kV is greater than the Lawson Criterion.
0-D Transport Model
nMu2/mom = Pin
3nT/heat = Pin - Prad
1/ mom = 1/ perp,i
1/ heat = 1/ perp,i + 1/ e
• Scales to reactor (u < VA, classical, Rm=4):
n=.6 1020, B=2.6T, a=1.1m, Pin=3MW
=> T=13keV, Ms=6, Pfusion=240MW
BPX and Reactor Scenarios:
Magnetic field is the key parameter
BPX Reactor
a (m) 1.2 1.1
B (T) 0.9 2.5
n (1020 /m3) 0.1 0.6
L/a 20 10
R/a 4 4
T (kV) 10 13
Ms 6 6
Q 8 70
PDT 4 250
1/MA 1.1 1.1
E 3 10
Measured plasma capacitance dependence on
plasma density agrees very well with MHD theory
0.00E+00
5.00E-05
1.00E-04
1.50E-04
2.00E-04
2.50E-04
3.00E-04
0 20 40 60 80 100
ne (1019
m-3
)
Cp (
F)
Circuit model yields an accurate measure of plasma
density
Theory
CP
Interferometer Density (1019 cm-3)
0-D Plasma Model
(1/2)CPVP2 = (1/2)u
2*VOL [energy stored in capacitor
= rotational kinetic energy]
CP = QP/VP [defines Cp]
u = VP/(aPB) [Vp and ap(plasma radial extent)
=> average ExB velocity, u]
Yields azimuthal speed, average density, momentum
confinement time.
Confirmed by Doppler spectroscopy, HeNe interferometer
To lowest order, MCX is a collisional, ideal MHD plasma
=> centrifugal confinement is the best explanation for x10 drops
• ~ 10cm << L => isotropic pressure, no loss cone physics
=> Braginskii equations
• ~ 0.2cm << a => Ideal MHD equations follow from Braginskii
=> B. p = - B.[nm u. u] to lowest order
• RHS = 0 => p( ) no pressure drop
• RHS from u|| (nozzle mirror losses) => Bernoulli => pressure drop ~ x2
• RHS from uExB => centrifugal stratification => pressure drop ~ exp[Ms2]
• RHS from CX friction (only non-Braginskii possibility)
=> plasma pressure drop only in neutral penetration layer <
10cm
Magnetic Flux Surfaces
Mirror Coil Low Field Coils
Z-pinch density profile approaches
laminarity with increasing Mach #
C1 is the laminar profile
(green).
C2-C6 are turbulent states
(blue) with respective
(turbulent) Mach numbers
0.3, 1.4, 2.2, 3.7, 4.8.
τCB vs. τFW
Edge dB/dt probes: fluctuations are consistent with
convection at local , dominant m = 2
0 1 105
2 105
3 105
4 105
0
200
400
600
0 20 400
5
10
V=34 km/s
Azimuthal Cross correlation analysis shows convection
5.5 11.5 18.0
24.0
30.0 37.0
0 10 20 30 40 50 601
0.5
0
0.5
1
CCF15v
CCF37v
CCF59v
CCF711v
CCF913v
CCF1115v
CCF131v
CCF153v
v
0 10 20 30 401
0.5
0
0.5
1
CCFA1v
CCFA2v
CCFA3v
CCFA4v
CCFA5v
CCFA6v
v
0 1 104
2 104
3 104
4 104
1
0.5
0
0.5
1
1.5
2
2.5
ACF7v
ACFVv
Vtsv
MV
t v0 1 10
42 10
43 10
44 10
41
0.5
0
0.5
1
1.5
2
2.5
ACF9v
ACFVv
Vtsv
MV
t v
t(s)
m=2 is dominant S-H Choi, Guzdar et al PoP 2008
HR -mode discovered
Rotation speed H 3
Mach number H ~ 3
Confinement time H ~ 3
-10
-8
-6
-4
-2
0
0 1000 2000 3000 4000 5000 6000 7000
Pla
sm
a V
olt
ag
e (
kV
)
Slug injection:
2D simulation, one-pass
~ 25% of slug
momentum
transferred to
plasma in one-
pass
Shamim et al PoP, POSTER
Wobble-free rotation ?
• Axial view of MCX plasma
• Phantom 7.1 camera
• t = 5 ms after breakdown
• dtexposure= 2 s
• 91,000 frames/s
Picture courtesy of
Ricardo Maqueda, PPPL
End view - 4 consecutive frames 2 μs exposure