Physics of acceleration, merging andcompression of frcs with a plasma liner

S. Woodruff, T. Ziemba, G. Votroubek, J. Slough, R. Milroy

February 13-16thInnovative Confinement Concepts Workshop

Austin, Texas

Abstract. The Inductive Plasmoid Accelerator (IPA) experiment at theUniversity of Washington aims to form two FRC plasmas and acceleratethem into an interaction chamber in which they are expected to reconnectand heat. The resulting FRC will be compressed by a plasma liner drivenby a fast coil. This paper outlines the physics of acceleration, reconnection,and compression expected to be encountered in this experiment and adiagnostic plan. The experiment will be constructed over the next year andshould be operational by fall. The experiment is a new magnetized targetfusion experiment and will have several unique features. The IPA offers theopportunity to study magnetic reconnection under highly energeticconditions (KE>Wmag~Etherm), with variable directional energies. This will bethe first time that a field reversed configuration will be used with a plasmaliner (usually compressed with a solid liner), and so the effects of symmetryand liner mass are considered. Success in this experiment depends stronglyon the timing issues, obtaining consistent breakdown and FRC mass: thesystem being installed to address timing will be shown in outline.

Magnetic targets will be accelerated, reconnected andcompressed to explore path between IFE and MFE.

(From Wurden et al 16th ANS TOFE Conference Madison, Wisconsin Sept. 15, 2004)

IPA similar to experiments by Wells, Ono and Brown

Wells reported keV ion temperaturesfrom impurity measurements,increasing as a function ofcompression coil bank voltage [1].

Counterhelicity merging ofspheromaks much faster than co [2].

~200eV ions spatially and temporallycorrelated with 3D reconnectionevents [3].

[1] D. R. Wells et al Phys. Rev. Lett 41 167 (1978)

[2] Ono et al Phys. Fluids Phys. Fluids B 5 3691 (1993)

[3] M. R. Brown et al Phys. Plasma 9 2079 (2002)

Inductive Plasmoid Accelerator (IPA) will be usedto study four physics issues in combination.

Interaction Chamber

1. What physics governs reconnection of twohigh energy FRCs?2. How does the reconnection rate scale withdirectional energy?3. How does directional energy becomeconverted to plasma thermal energy?4. How is a FRC radially compressed?

AccelerationSections

2m

Prototype Prototype

InteractionChamber

1021-1023Density, n

20-100eVElectron temp, Te

Analytic physics of the field reversed configurationin simple geometries.

[4] M. Tuszewski, "Field Reversed Configurations ", Nucl.Fusion 28, 2033 (1988)

[5] W. T. Armstrong et al Phys. Fluids 24 2058 (1981)

Analytic equilibria for frc -variousforms - this is the ‘Hills Vortex’equilibrium €

Δφ = πrs2Be

Parameters:

Diamagnetism€

< β >=1− xs2

2xs = rs /rc

€

s = rdrrsρiR

rs

∫ ~ rs< ρi >

~ S*

10

€

τE (µs) ~ 0.5τN ~0.5R2

ρie (cm)€

ψ = (−3Br2 /4a2)(a2 − R2) for r < rs

Initial experiments on prototype (old MAP experiment)address FRC formation and particle control.

The formation -accelerator involves along solenoid comprisedof many separate coils,which are pulsed oneafter the other toproduce a travelingmagnetic wave, whichalso reverse thedirection of the appliedvacuum field.

Above. Puff and gas flow modeledin 2D to obtain requisite densities.Below. Filtered emission viewingplasma created by cascaded arcsource and reversal fields.

Excluded flux (Wb)

FRC will reach ~200km/s (20cm/µs) during formation

[6] R.D. Milroy and J.U. Brackbill, "Numericalstudies of a field-reversed theta-pinch plasma", Phys.Fluids 25, 775 (1982)

2D MHD simulationsshow formation by asudden reversal ofexternal field [1].

Acceleration occursduring formation aseach coil is energized.

Quarter cycle risetimes of the coils are~1µs.

Reconnection of two FRCs

Two merging FRCs, expected toproceed in similar manner toforced reconnection inspheromaks with oppositelydirected helicities [7].

Particle energies should scale asthe reconnection electromotiveforce (EMF)

E ~ ∫ E · dl = vBL

where L is a characteristic lengthof the system along the electricfield [8].

2D and 3D models will be used toexplore reconnection in IPA.

[7] E. Belova - Invited Talk at DPP APS 2005

[8] Makishima, K. 1999, Astron. Nachr., 320, 163

Reconnection region flux function:

Current sheetsform inplasmas duringreconnection.

Magnetic fieldline tension pullsplasma out ofreconnectionregion.

€

JxB =1/µ0(B.∇)B

€

ψ(x,y) =1/2B0(x2 − y 2)

Plasma flows inward with velocity, v.

Classical reconnection schematic:

Reconnection will be ‘fast’ for merging FRCs.

[9] Priest and Forbes “Magnetic Reconnection” Cambridge University Press (2000)

[10] M. Yamada et al Phys. Plasmas 4 1936 (1997)

For fast (Me>RMe1/2) driven,time-dependent and non-uniform reconnection, incollisional plasmas the mostpromising models entailPetschek-like reconnection [9-10].

First order constraints onstrongly flowing, weak fieldreconnection will be fluid-likein which the reconnection ratewill be governed byincompressible flow outwardsfrom the region.

~10Me=ve/vA

105ms-1vext

~1Rme=vA/vd=vAL/η

~105(Ωm)-1σSpitzer

0.01cmc/ωpi

1021 to 1023m-3n

Expected parameters:

The implosion of a liner using a theta or z pinchcan be described by the following equation ofmotion:

where mL is the liner mass/unit length = ρ2πr0d0with d0 being the initial liner thickness. BL is themagnetic field outside the liner. As will be seen inthe numerical calculations, the coil current for thetheta pinch implosion of the liner is roughlyconstant even though a sinusoidal currentwaveform would be obtained in vacuum.

IPA will provide the first test an imploding plasmaliner on an FRC target.

In a staged Z-Pinch, an annular plasmaliner is accelerated toward the axis ofsymmetry and collapsed onto a co-axialdeuterium-tritium (DT) fuel [11].

Issues for plasma liners include:stability during implosion andmaximum compression ratio;achievable velocity; liner thicknessneeded for required velocity; compositemulti-layer liners; liners with shapesand variable thickness to achieve 3-Dcompression [12]

[11] Phys.Rev.Lett.74, p. 7141(1995)[12] Siemon et al MTF Roadmap 1998

1D model: main parameters vary steeply as a functionof wall radius.

[13] R. L. Spencer, M. Tuszewski, and R. K. Linford Phys. Fluids 26 1584 (1983)

€

ddt(pρ−γ ) = 0

l

r

T

n

B

a.u.

Elongated FRCs reduce to1D models - used here todetermine physics ofcompression [13].

Adiabatic compressionassumes:

implying conservation ofentropy.

Scaling laws for γ=5/3 areshown in the table andfigure.

2D MHD simulations of FRC compression showstrong convergence, and axial contraction.

FRC compressionproceeds by impositionof strong magneticfields, typically on a 1µstime-scale.

Field strengths increaseby x10 during thecompression, withcorresponding increasesin temperature.

Stability remains thecritical issue duringcompression, whichmight be addressed with3D MHD simulations inthe NIMROD model.

Diagnostic summary.

[14] G. A. Wurden, T. P. Intrator, D. A. Clark, R. J. Maqueda, J. M. Taccetti, F. J. Wysocki, S. K.Coffey, J. H. Degnan, and E. L. Ruden, Rev. Sci. Instrum., 72, 552 (2001)

Diagnostic set for the IPA willinclude some standarddiagnostics for FRCs [14], butalso a set for inspecting thereconnection region (e.g. ionenergy measurements in thereconnection region).

TeLangmuir tips

fE(n0), TiNeutron detector (Scintilator)

Prad (t)Bolometer (Sxray)

TiMonochrometer

Excluded fluxFlux loops

fE(ions)Retarding Grid Energy Analyzer

Ti, vrotationalVUV Spectrometer

ne(1023 --> 1025m-3)Interferometer

n0H-alpha

BMagnetic B-dot probes linear, azimuthal

ParameterDiagnostic

TeLangmuir tips

fE(n0), TiNeutron detector (Scintilator)

Prad (t)Bolometer (Sxray)

TiMonochrometer

Excluded fluxFlux loops

fE(ions)Retarding Grid Energy Analyzer

Ti, vrotationalVUV Spectrometer

ne(1023 --> 1025m-3)Interferometer

n0H-alpha

BMagnetic B-dot probes linear, azimuthal

ParameterDiagnostic

In total, ~60 datachannels will be usedwith 20MHzresponse for theformation andtranslation, 100MHzfor the compression.

Diagnostics for formation/acceleration phase.

Plasma breakdown: H-alpha, monochrometers,

Dual pass HeNe interferometer with path through portdownstream on prototype will be used on IPA.

Equilibrium/translation: flux loops and B-dot probesin the z-direction and in the azimuthal direction togive indication of symmetry. Internal probes couldmeasure current distribution in the FRC.

Combined with an excluded flux array, a single chordof side-on interferometry provides a good estimate ofthe separatrix particle inventory N and of the particleconfinement time Assuming radial equilibrium, thesame combination permits estimation of the totaltemperature Te + Ti.

Mach probes with two collecting plates have beenused for measurements of the parallel and theazimuthal flow velocities with respect to thestationary magnetic field.

µ0 J = ∇× B =1r

ˆ r r ˆ θ ˆ z d /dr d / dθ d / dz

Br rBθ Bz

Jz =1

µ0rd rBθ( )

dr and Jθ =

−1µ0

dBzdr

.

Diagnostics for reconnection phase.

To survey the reconnection physicsat high energy - unlikely to haveability to insert probes (they willbe destroyed by heat flux tosurface) [15].

Main diagnostics will be RGEA[16] mounted in the reconnectionplane, as per SSX, and fastresponse time field probesmounted on the outside of thereconnection region.

Need n (interferometry), v(spectroscopy), and B (externallymounted probes) in order todifferentiate between reconnectionregimes.

[15] J. Slough and K. Miller Rev. Sci. Instrum., Vol. 72, No. 1, January 2001

[16] T. J. Dolan “Fusion Research” Chapter 10 Pergamon Press 1982

Diagnostics for compression phase.

Ion temperature determined by Wellsfrom doppler broadening of impuritylines (by use of VUV spectrometer).

Neutron flux using scintillatordetectors: Energetic neutrons incidenton organic liquids and plastics produceenergetic recoil protons by elasticcollisions. The protons cause thescintillator to emit photons, which inturn eject photoelectrons from thecathode of a photomultiplier tube,which amplifies the current pulse.

Density will be obtained by end-oninterferometry.

Summary

New experiment being constructed at the University ofWashington: Inductive Plasmoid Accelerator, aims to answer:

1. What physics governs reconnection of two high energy FRCs?

2. How does the reconnection rate scale with directional energy?

3. How does directional energy become converted to plasma thermal energy?

4. How is a FRC radially compressed (and how does it heat)?

Diagnostic set being designed.

Initial formation experiments on single stage.

Parts arriving and space allocated: pump-down of 2nd stage in onemonth, initial results to report by APS.

References

[1] D. R. Wells et al Phys. Rev. Lett 41 167 (1978)[2] Ono et al Phys. Fluids Phys. Fluids B 5 3691 (1993)[3] M. R. Brown et al Phys. Plasma 9 2079 (2002)[4] M. Tuszewski, "Field Reversed Configurations ", Nucl. Fusion 28, 2033 (1988)[5] W. T. Armstrong et al Phys. Fluids 24 2058 (1981)[6] R.D. Milroy and J.U. Brackbill, "Numerical studies of a field-reversed theta-pinch plasma",Phys. Fluids 25, 775 (1982)[7] E. Belova - Invited Talk at DPP APS 2005[8] Priest and Forbes “Magnetic Reconnection” Cambridge University Press (2000)[9] M. Yamada et al Phys. Plasmas 4 1936 (1997)[10] Makishima, K. 1999, Astron. Nachr., 320, 163[11] Phys.Rev.Lett.74, p. 7141(1995)[12] Siemon et al MTF Roadmap 1998[13] R. L. Spencer, M. Tuszewski, and R. K. Linford Phys. Fluids 26 1584 (1983)[14] G. A. Wurden, T. P. Intrator, D. A. Clark, R. J. Maqueda, J. M. Taccetti, F. J. Wysocki, S. K.Coffey, J. H. Degnan, and E. L. Ruden, Rev. Sci. Instrum., 72, 552 (2001)[15] J. Slough and K. Miller Rev. Sci. Instrum., Vol. 72, No. 1, January 2001[16] T. J. Dolan “Fusion Research” Chapter 10 Pergamon Press 1982