Magnetic Intervention: Modeling and Experiment

Magnetic Intervention: Modeling and Experiment D. V. Rose, D. R. Welch, T. C. Genoni,C. Mostrom, T. P. Hughes, N. Bruner, C. ThomaComputational Physics GroupVoss Scientific, Albuquerque, NMA. E. Robson, J. Giuliani, Jr., J. D. Sethian, D. D. Hinshelwood, D. Mosher, R. J. Commisso, F. C. Young, P. F. OttingerPlasma Physics Division, Naval Research Laboratory HAPL Workshop, ORNL, March 21, 2006

Outline • Magnetic intervention • brief review • R. Pechacek experiment modeling • brief review of simulation work • Proposed pulsed power magnetic intervention experiment • design & modeling • Computational modeling for IFE-scale magnetic intervention • plans / outlook

Use an applied magnetic field to intervene with the flow of energetic ions produced in the target explosion to limited areas of the chamber Recover a portion of this directed ion energy and convert it into electrical energy Improve chamber first wall lifetime by eliminating ion bombardment Direct ion energy conversion improves power plant efficiency Magnetic Intervention – Concept & Benefits:

Basic Schematic: Magnetic Intervention Magnetic field formedby a pair of current-carrying rings Energetic ionsproduced during target implosion C L “Point” Cusp Chamber first-wallprotected from ionbombardment bymagnetic field “Ring” Cusp

A Simplified View of Basic Magnetic Intervention “Physics” Ampere’s Law vx bz(x) r x Electron sheath currentinduced, ex slows ions Ohm’s Law vx bz(x) r x Gradient in ey inside sheath induces reduction in bz Faraday’sLaw vx bz(x) r x

R. Pechacek experiment:* • Chamber wall radius = 30 cm • External field coils, 70 cm diam, 70 cm separation. 2.0 kG at ring cusp, 4.4 kG at point cusp. • 2x1019 D2 ions produced from cylindrical target of 1-mm diam., 1-mm length *R. E. Pechacek, et al., Phys. Rev. Lett. 45, 256 (1980) & NRL Memorandum Report 4162, Feb. 15, 1980.

Measurements demonstrated magnetic compression and relaxation of field lines: Measurement of ion current escaping (with B=0) gives initial ion distribution (next slide)

Use experimentally measured current-density from shot without applied B-field to determine approximate source distribution function:

Sample from this calculated distribution in an LSP orbit calculation, assuming a 4-cm radius, uniform density ion cloud with radially directed velocities.

Initial EMHD simulation results illustrate aspects magnetic intervention dynamics. 0 ms 3 ms 6 ms |B| ni

Simulation result: Magnetic field swept back too quickly, takes too long to snap back into place. Plasma diffuses intomagnetic field artificially at later times, reducing themagnetic pressureavailable to pushplasma out of chamber Early time compressionof magnetic field drivenby artificiallyhigh electricfield in simulatedsheath

P. Parks model* (analytic) and A. Robson** model (2D “shell” calculation) both in agreement with experiment. P. Parks model (45 deg)A. Robson model (27 deg) *P. Parks, Phys. Plasmas (2005) **A. E. Robson, various HAPL presentations

Pulsed Power Magnetic Intervention Experiment(s) • The need for near-term, cost effective experiments to test physics and computational modeling of the MI concept has been identified. • Pulsed power generators producing directed energy ion beams and/or plasmas is one option being explored.

Gamble II, completed in 1970*, is the prototype of all waterline capacitive storage simulators 1.5 TW, ±1.5 MV, 1 MA, 60 ns Oil-insulated Marx0.5 MJ, 5 MV Water-filled coax (capacitive power conditioning) Vacuum load region *Shipman, IEEE Trans. Nucl. Sci. 1971

The high-sensitivity, 2-color, laser interferometer is a unique capability for measuring plasma and gas densities. cw two-color interferometer 1.064, 0.532 m Pulsed nitrogen laser 0.337 m (Schlieren photography)

A small-radius pinch-reflex diode (PRD), designed as an ion source for self-pinched ion beam transport experiments,* is a suitable proton source for the magnetic intervention experiments. cathode ion current monitor 3 cm ion beam centerline anode foil Kimfol vacuum 1 Torr air * P. F. Ottinger, et al., Phys. Plasmas 7, 346 (2000). P. F. Ottinger, et al., Nucl. Instrum. Meth. Phys. Res. A 464, 321 (2001).

Gamble II Experiment: Schematic Single-turn coil 30 cm Gamble II 20 cm C L 70 cm 10-30 cm A portion of the total proton beam enters the chamber through an aperture.

C L Physical Parameter Definitions, nominallydefined inside point cusp, on axis:

Dimensionless Parameters: Pressure scale Length scales Time-scales

Point-Cusp Physics Scaling

Sample Simulation Results: Mono-energetic beam, Gamble II “Lite” parameters: • Bz = 1.6 kG • magnetic coil position: r_mag=20 cm, z_mag=50 cm • mono-energetic proton beam waveform (slug/slab) • 20 degree beam opening angle • r_b (injected)=5 cm • Injected proton current ~ 10 kA Fully EM, kinetic PIC simulations in 2D (r,z) coordinates.

Simulation geometry and parameters for a mono-energetic test case of Gamble II “Lite”: Magnetic field dueto solenoid, 6 cm long,20 cm radius, 1.6 kG onaxis. Conducting torusexcludes artificially high fields near coils. Electrons (blue)pulled from entrance“foil” via space-charge-limitedemission out to r=5.5 cm Beam protons (red)injected with a 20 deg.opening angle, 5-cm radius,uniform current density.

Initial Magnetic Field Topology:

Protons Electrons Snapshots of particle positions and energies show :(1) electron sheath formation(2) ion energy loss 30 ns 40 ns 20 ns Electrons Protons

np |B|

The dynamics of the electromagnetic calculation (left) contrast sharply with a simple orbit calculations (right): np np Orbit calculation Full “EM” PIC simulation

Sheath thickness can be resolved for the “Lite” parameter regime: |B| Electrons, 40 ns |E| ni

The case for a pulsed magnetic intervention experiment, i.e., Gamble II “Lite”: • Relatively inexpensive  • Compliments the results of the “Pechacek” experiment • Accesses important “point cusp” interaction physics • Enables the generation of significant magnetic compression, demonstrating energetic ion stopping (the “45 degree” push, i.e. “intervention”) • 2D (r,z) physics explored via PIC simulation. • [3D (r,q,z) PIC modeling may also be feasible] • Issues yet to be explored: • Experimental Diagnostics (temporal and time-integrated) • Final experimental layout (vacuum vessel dimensions, ports, coils & banks)

The Gamble II “Lite” experiment would not study: • Ring cusp physics (critical since most of the ions would leave via this route)  • Multiple ion bounce physics issues (requires a true cusp field, i.e., Pechacek) • Long-time scale physics (single shot) • Multi-pulse operation • …

Computational Modeling Plans: • Continue to explore development and implementation of EMHD-like models for magnetic intervention: • Earlier work with anomalously high resistivity and background plasma density used to examine the Pechacek experiment. This will be continued (see next slide) • New developments include 2D field solver of John Giuliani (coding underway). • New work by Dale Welch has explored Eulerian-Lagrange remap to deal with steep density gradients and large densities.

There exist a variety of computational approaches that may be adaptable to the magnetic intervention problem: • Gyro-kinetic or guiding-center electron models that preserve electron response to field and ion dynamics • EMHD-like models with dissipation that convect and damp anomalously high electric fields • Push EM implicit kinetic modeling further into MHD regime with finer gridding, more particles at plasma/vacuum interface • Adaptive-mesh strategies for both EMHD and hybrid EM that follow the plasma-magnetic field interface

Summary: • A low-cost pulsed power experiment is being designed to experimentally test some aspects of the magnetic intervention concept • Computational algorithms capable of handling long-time-scale, high-plasma-density, high-b physics for non-Maxwellian plasmas are being developed. • Analytic modeling and simplified computational treatments continue to add insight into the physics of magnetic intervention.

Backup material:

Solid wall, magnetic deflection • Cusp magnetic field imposed on to the chamber (external coils) • Ions compress field against the chamber wall: (chamber wall conserves flux) • Because these are energetic particles, that conserve canonical angular momentum (in the absence of collisions),Ions never get to the wall!! • Ions leak out of cusp ( 5 sec), exit chamber through toroidal slot and holes at poles • Magnetic field directs ions to large area collectors • Energy in the collectors is harnessed as high grade heat Coils Mag Field Particle Trajectory Toroidal Slot Pole A.E. Robson, "Magnetic Protection of the First Wall," 12 June 2003

EMHD algorithm for LSP under development • Quasi-neutrality assumed • Displacement current ignored • PIC ions (can undergo dE/dx collisions) • Massless electron fluid (cold) with finite scalar conductivity • Only ion time-scales, rather than electron time-scales, need to be resolved. • Model is based on previous work, e.g., Omelchenko & Sudan, JCP 133, 146 (1997), and references therein. • Model used extensively for intense ion beam transport in preformed plasmas, ion rings, and field-reversed configurations.

EMHD model equations: Currents are source terms for curl equations: Ohm’s Law for electron fluid: Scalar conductivity can be calculated from neutral collision frequencies:

Model Constraints: Convergence: Alfven Courant: Dominant Collision Frequency: Ion Courant:

Simple estimate of “stopping distance” for expanding spherical plasma shell: (in MKS units) Assuming plasma expansion stops for b ~ 1, then: This results is consistent with simulation results for n0 = 1011 – 1014 cm-3. vi = 0.01c Bo = 2 T protons

A Look at Diamagnetic Plasma Penetration in 1D

1D EMHD model* • The model assumes local charge neutrality everywhere. • Electrons are cold, massless, and with a local ExB drift velocity • “Beam” ions are kinetic, with an analytic perpendicular distribution function. Analysis is “local”, meaning that Bo isapproximately uniform with in the ionblob. *Adapted from K. Papadopoulos, et al.,Phys. Fluids B 3, 1075 (1991).

Model Equations: Ions Penetrating a Magnetized Vacuum Quasi-neutrality: Electron velocity: Continuity: Ion Distribution: Ion Density: Ion Pressure Force Balance: Pressure Balance:

Magnetic field exclusion: Assume a perpendicular ion energy distribution given by: Assume a 1D density profile: The ion beam density and pressure are then given as: The potential and electric fields are then: From pressure balance, this gives a magnetic field profile of:

Sample Result: (MKS units) In the limit that the argument of the square root is > 0,this gives a simple diamagnetic reduction to the applied field.I assume that when the argument of the square root IS < 0,then the applied field is too wimpy to impede the drifting cloud. b = 0.005; x0 = 1; nb0 = 1.0*10^(17)*(10^6); nb[x_] := nb0*Exp[-((x - x0)^2)/(b^2)]/(x0^3); Plot[nb[x], {x, -0.02, 2*x0}, PlotRange -> {0, 2*nb0/(x0^3)}]; B0[x_] := (2/5)*x; q = 1.6*10^(-19); Tb = (0.5*4*1.67*10^(-27)*((0.043*3*10^8)^2))/q; mu0 = Pi*4*10^(-7); xmax = ((25/4)*2*mu0*nb0*q*Tb)^(1/5); Print["Tb(eV) = ", Tb]; Print["xmax (m) = ", xmax]; By[x_] := B0[x]*(Max[1 - 2*mu0*nb[x]*q*Tb*(B0[x])^(-2), 0])^(0.5); Plot[(By[x]), {x, 0, 2*x0}]

Bertie’s test case uses 120 MJ of 3.5 MeV 3He++ ions with an initial radius of 26 cm. 500 ns 400 ns 300 ns 200 ns 100 ns Shell surface at 20 ns intervals: Ring orbits plotted every 2 ns:

LSP run: bob9b.lsp Sigma = 1e14 (1/s) Ne-background=2e14 (cm-3) Non-Maxwellian ion distribution Initial magnetic field magnitude 0.00015 ms 2-cm initial plasma radius (uniform density)

Magnetic Intervention: Modeling and Experiment