Scaling of the Sheared-Flow Stabilized Z-Pinch:The Fusion Z-Pinch Experiment "FuZE"

B. A. Nelson, U. Shumlak, E. L. Claveau, R. P. Golingo,M. C. Hughes, M. P. Ross, and T. R. Weber

University of Washington

H. S. McLean, A. E. Schmidt, and K. K. TummelLawrence Livermore National Laboratory

Supported by U.S. DoE and ARPA-E

EPR Workshop 2016February 26, 2016

Nelson et al. ZaP Scaling and FuZE EPR 2016 1 / 20

Sheared Flow Can Stabilize a Z-Pinch

The ZaP experiment used sheared-flow stabilization to producelong-lived Z-pinches

Quiescent plasmas last thousands of instability growth times andseveral flow-through times

Low MHD mode activity is correlated with sheared plasma flow

Quiescent plasmas can be maintained as long as the plasmasource and current persists

The new Fusion Z-pinch Experiment “FuZE” will studysheared-flow stabilization scaling to higher densities

Nelson et al. ZaP Scaling and FuZE EPR 2016 2 / 20

ZaP and FuZE Personnel

UW Faculty & Staff Undergraduate StudentsUri Shumlak (PI) Johnathon R. BarhydtBrian A. Nelson (Co-PI) Deianeira L. CaudleRaymond P. Golingo Shawn A. DotyTobin R. Weber Eleanor G. Forbes

Edwin L. H. LiLLNL Staff Michael W. O’DellHarry S. McLean (PI) Leanne L. SuAndréa E. Schmidt (Co-PI) Ryan M. TownsendKurt K. Tummel

Graduate Students CollaboratorsMichal C. Hughes Daniel J. Den Hartog (U Wisc)Michael P. Ross Charles W. Hartman (LLNL)Elliot L. Claveau Masayoshi Nagata (U Hyogo)Bonghan Kim

Nelson et al. ZaP Scaling and FuZE EPR 2016 3 / 20

Sufficient Sheared-flow Stabilizes a Z-Pinch

Linear stability applied tomarginally-stableKadomtsev equilibrium

−d ln pd ln r

=γ

2 + γβ

In the no-wall limit,rw > 4a, stability seen for

dVz

dr≡ V ′z ≥ 0.1kVA

Destructive interferenceand phase mixing fromsheared flow

Shumlak and Hartman, PRL 1995

Nelson et al. ZaP Scaling and FuZE EPR 2016 4 / 20

Non-radiallly-uniform Acceleration Process ProducesSheared Flow Z-pinch

Gas is injected andcapacitor is discharged.

Plasma acceleratesdown the coaxialaccelerator until itassembles into aZ-pinch plasma alongthe axis.

Inertia and gun currentsmaintain the flowingplasma state until theaccelerator plasmaempties or currentdiminishes.

Nelson et al. ZaP Scaling and FuZE EPR 2016 5 / 20

ZaP Experiment and Diagnostics

ZaP Z-pinch with sheared-flow stabilization

1 m acceleration & 1-massembly regionsAxial and azimuthal surfaceprobe arraysHeterodyne-quadrature HeNeinterferometry (4 chords)

Plasma current and voltagemeasurements20-chord ion DopplerspectroscopyDigital holographicinterferometryFast-framing camera

Nelson et al. ZaP Scaling and FuZE EPR 2016 6 / 20

ZaP Operating Parameters

Parameter Symbol ValueCapacitor bank energy Ecap 144 kJ (max)

Charge voltage Vc 10 kV (max)Plasma current Ip 480 kA (max)

Pinch radius a 0.5–1 cmPinch length `p 50–126 cm

Electron density ne 1016–1017 cm−3

Plasma temperature Te + Ti 150 – 250 eVPlasma lifetime τp 20 – 100 µs

Working gas is hydrogen(sometimes with CH4 as a dopant)

Nelson et al. ZaP Scaling and FuZE EPR 2016 7 / 20

Magnetic Fluctuations Diminish After Pinch Forms

“Quiescent period” defined for normalized azimuthal mode dataB1/B0 ≤ 0.2 (displacement of a plasma radius).

' 37 µs quiescent period(Instability growth time ' 20 ns; flow through time ' 10 µs)

Nelson et al. ZaP Scaling and FuZE EPR 2016 8 / 20

Flow Profile is Correlated to Plasma Stability

τ < 0, plasma assembly, axialplasma velocity is high anduniform, v ′z ' 0− 4× 106 s−1

0 ≤ τ ≤ 1, quiescent period, thevelocity profile is high at theplasma edge and lower at theaxis, v ′z ' 7− 12× 106 s−1

At a point during the quiescentperiod, the edge velocity slows sothe velocity is higher at the axisthan the edge.

τ > 1, end of quiescent period,the plasma velocity profile is low& uniform, v ′z ' 0− 6× 106 s−1

Theoretical growth time is ' 20 nsShear threshold is ' 5× 106 s−1

Nelson et al. ZaP Scaling and FuZE EPR 2016 9 / 20

Experimental Modifications Confirm the No-wall Limit

Close-fitting conducting walls can stabilize, providing an alternativeexplanation to the observed stability.To test the no-wall limit, a section of the outer electrode is insertedwhich contains large perforations.

Nelson et al. ZaP Scaling and FuZE EPR 2016 10 / 20

ZaP Shows Evidence for Long-length Pinches

Magnetic data up to 86 cm frominner electrode show quiescentpinch of nearly constant field

Interferometer data 57 cm frominner electrode show density

peaked on axis

0.00

0.05

0.10

0.15

0.20

B0 [T

]

z=34 cm

110505021

0.00.51.01.52.0

∫ ned` [

1021

m−

2]

z=40 cm

y=0 cmy=1.7 cm

0 20 40 60 80 100Time [µs]

0.00.20.40.60.81.0

B1/B

0

z=34 cm

End of inner electrode is at z=-17 cm

Nelson et al. ZaP Scaling and FuZE EPR 2016 11 / 20

Axial Bθ Profile Shows Long-length Z-pinch

∇× B = µ0J⇒ ∂Bθ∂Z

= −µ0JR

Long-length axial current structures (∂Bθ∂Z ' 0) observed throughout the

assembly region during the quiescent period.

150 100 50 0 50 100Z [cm]

0.0

0.1

0.2

0.3

0.4

0.5

Bθ [

T]

Assembly RegionJR '0 During Q Period

Mean Bθ and STD

Pulse 100616037

t=14.4 ust=19.4 ust=24.4 ust=42.4 us

Acceleration RegionSignificant JR

Plasma Initiationand Rundown

Nelson et al. ZaP Scaling and FuZE EPR 2016 12 / 20

Viscosity Shear Damping Time Allows Long PinchesViscous damping time:

τµ ' ρL2v/µ

Unmagnetized µ (SpitzerEq. (5-54) in SI–eV units):

µ = 1.52× 10−25 T 5/2A1/2i

Z 4 ln Λ

magnetized µ⊥ (Eq. (5-55)):

µ⊥ = 2.89× 10−4 A3/2i Z 2n2

i ln Λ

T 1/2i B2

µ⊥ and τµ adiabatic scalings areindependent of Ip (Hughes et al.,APS 2015)

0 2 4 6 8 100.00.51.01.52.02.53.03.5 I0 =250.0 kA, a=1.0 cm, T=100 eV, Lv=0.3 cm

n (1017 cm−3 )B (T)

0 2 4 6 8 1010-1

100

101

102

103

104

ωci/νii

0 2 4 6 8 10r (cm)

10-510-410-310-210-1100101102103

τ µ (µ

s) τµ (µs) τ no Bτ

⇒ Viscous damping time >∼ 1 m flow-through timeNelson et al. ZaP Scaling and FuZE EPR 2016 13 / 20

Summary of ZaP Results

ZaP demonstrates evidence of flow-shear stabilization of a Z-pinch:MHD stability correlated with sheared velocity

Stability lasts as long as there is flow shear, plasma in theacceleration region, and the power supply current persists

Stability period increased with increasing pinch length

Removal of a large section of the outer wall did not affect stability

Viscous damping time greater than flow-through timeAdiabatic scaling of µ⊥ and τµ independent of Ip

Nelson et al. ZaP Scaling and FuZE EPR 2016 14 / 20

Scaling to Higher Currents: The FuZE Experiment

Adiabatic pinch scaling for a Bennett equilibrium:

∂

∂t

( pnγ

)=

∂

∂t

((1 + Z ) kT

nγ−1

)= 0; (1 + Z ) NkT =

µ0I2

8π

FuZE is designed as an intermediate step towards asheared-flow-stabilized Z-pinch fusion reactor

Nelson et al. ZaP Scaling and FuZE EPR 2016 15 / 20

FuZE Program GoalsFunded Through the ARPA-E ALPHA Program

100-cm-long acceleration & 50-cm-long assembly region

Extend ZaP sheared-flow stabilized Z-pinch results to highercurrents, densities, and temperatures

Improved gas puff fueling (SSPX valves)Improved pumping capacity (additional surge tank)More flexible power supply capability (SSPX power supplies)

Operation with H2 and D2 gas mixturesIncrease fraction of D2 to study neutron production

Detailed kinetic calculations, including neutronicsLSP PIC code to include kinetic particles (Schmidt and Tummel)

Nelson et al. ZaP Scaling and FuZE EPR 2016 16 / 20

ZaP and FuZE Parameters

Parameter Symbol ZaP Value FuZE Design(Nominal)

Capacitor bank energy Ecap 70-110 kJ 90(+) kJCharge voltage Vc 7–9 kV 20(+) kVPlasma current Ip 100–200 kA 300–500(+) kAPinch current Ipinch 50–100 kA 150–300 kAPinch radius a 0.5–1 cm < 1 mmPinch length `p 50–126 cm 50 cm

Electron density ne 1016–1017 cm−3 ∗ 1019 cm−3

Plasma temperature Te + Ti 100 eV 800–1000 eVPlasma lifetime τp 40 µs TBD

Working gas H2 H2 & D2 mix

∗ne = 1018 cm−3 and a=0.3 cm already achieved in ZaP-HDNelson et al. ZaP Scaling and FuZE EPR 2016 17 / 20

FuZE On Track for First Plasma in Spring 2016

More flexible LLNL power supply and gas-fueling valves50-cm-long Rectangular Viewports

HHHHj

LLNL Puff Valves

����

LLNL Cap Bank:• 24 × 18.5 µF at 20 kV• 12 × D-size ignitrons• Diode crowbar and isolation

between ignitrons

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Pumping Systemand Surge Tank

��

Nelson et al. ZaP Scaling and FuZE EPR 2016 18 / 20

FuZE LSP Code Kinetic Simulations are UnderwayEvolution of a Bennett profile (Kurt Tummel and Andréa Schmidt of LLNL)

Nelson et al. ZaP Scaling and FuZE EPR 2016 19 / 20

Summary & Future Work

Summary:ZaP shows long-length (1 m) Z-pinches, stable for thousands ofinstability growth times and several flow-through times

Stability correlated with presence of sheared-flow, a source ofaccelerated plasma, and power supply current

Stability shown to not be affected by conducting wall

Future Work:Fusion Z-pinch experiment, “FuZE”, will study scaling offlow-shear stabilized Z-pinches to higher densities andtemperatures

First plasma Spring 2016

Nelson et al. ZaP Scaling and FuZE EPR 2016 20 / 20