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