A Physics Exploratory Experiment on Plasma Liner Formation Y

Preparing to load PDF file. please wait...

0 of 0
A Physics Exploratory Experiment on Plasma Liner Formation Y

Transcript Of A Physics Exploratory Experiment on Plasma Liner Formation Y

A Physics Exploratory


on Plasma Liner Formation

Y.C. Francis Thio

NASA Marshall Space Flight Center, Huntsville, AL 35812

Charles E. Knapp, Ronald C. Kirkpatrick, Richard E. Siemon Los Alamos National Laboratory, NM Peter Turchi

Air Force Research Laboratory, Kirtland AFB

Abstract Momentum flux for imploding a target plasma in magnetized target fusion (MTF) may be delivered by an array of plasma guns launching plasma jets that would merge to form an imploding plasma shell (liner). In this paper, we examine what would be a worthwhile experiment to do in order to explore the dynamics of merging plasma jets to form a plasma liner as a first step in establishing an experimental database for plasma-jets driven magnetized target fusion (PJETS-MTF). Using past experience in fusion energy research as a model, we envisage a four-phase program to advance the art of PJETS-MTF to fusion breakeven (Q - l). The experiment (PLX) described in this paper serves as Phase 1 of this four-phase program. The logic underlying the selection of the experimental parameters is presented. The experiment consists of using twelve plasma guns arranged in a circle, launching plasma jets towards the center of a vacuum chamber. The velocity of the plasma jets chosen is 200 kin/s, and each jet is to carry a mass of 0.2 mg - 0.4 mg. A candidate plasma accelerator for launching these jets consists of a coaxial plasma gun of the Marshall type.

1. Introduction

Magnetized target fusion (MTF) attempts to combine the favorable attributes of both magnetic confinement fusion (MCF) and inertial confinement fusion (ICF), thus providing potentially a lowcost, rapid pathway towards practical fusion (1-5_.

In MTF, a magnetized plasma (designated as the target) is compressed inertially by an imploding

shell. The imploding shell may be solid, liquid, gaseous, or a combination of these states. The

presence of the magnetic field in the target plasma suppresses the thermal transport to the plasma

shell, thus lowering the imploding power needed to compress the target to fusion conditions. This

allows the required imploding momentum flux to be generated electromagnetically

with off-the-shelf

pulsed power technology. Practical schemes for standoff delivery of the imploding momentum flux

are required and are open topics for research. One approach for accomplishing this consists of using a

spherical array of plasma jets to form an imploding spherical plasma shell (6) (Figure 1).

The use of plasma jets to implode a target plasma has its root in impact fusion (7' 8). Impact fusion would have been a very attractive approach to ICF except for want of a suitable driver (a 0. l-g solid

projectile at 200 km/s). The approach is currently being revisited in its modern form in the context of

magnetized target fusion (6). Instead of only two solid projectiles, the required momentum flux is

spread over as many as 60 plasma jets traveling at approximately the same velocity. The plasma jets

are produced in pulsed electromagnetic

plasma accelerators using off-the-shelf electromagnetic

pulsed power. Their kinetic energy is accumulated over a spatial extent of about a meter in the

plasma gun and over a time interval of several microseconds using the ponderomotive

electromagnetic lO0-nanosecond

Lorentz force (j x B). Their kinetic energy is deposited in the target abruptly in a time scale and in a distance of a few centimeters. As a result, the imploding power

flux density is amplified by three to four orders of magnitude.


We notethat,unlike laserdriven ICF, the imploding energyis carrieddirectly by theplasmajets. In laserdriven ICF, the laserenergyneedsto beconvertedinto plasmaenergyat thetargeteither directlyor indirectly. Giventhatthe hydrodynamicefficiencyof convertingthephotonenergyinto directedimplosionenergyis about10%andtheefficiency of producingthe laserbeamsfrom electricity is lessthan20%,the overall"wall-plug" efficiencyof the laserdriver is lessthan2%. In the caseof the plasmajets for MTF, the equivalentdriver efficiency,the "wall-plug" efficiencyof plasmaguns,may beashigh as50%. Thus,laserdriven ICF may requirea fusiongain atleast25 times greaterthanMTF just to recoverthe energylost in thedriver.
With greatlyimprovedtargetdynamicsaffordedby the magnetizationof thetargetplasma,taking advantageof the theoreticalandexperimentaal dvancesin spheromakandFRC physicsin the last two decadesM, TF promisesto provideanaffordablepathwaytowardsfusionenergyon Earth_2a) nd fusion spacepropulsion(9).


The target plasma : A plasma ball, about 10 cm in diameter, formed by merging two plasma rings carrying magnetic fields.
PVlealsomciaty gurnequliaruedn:ches - t2h0e0 pklmas/ms.a jets. I
Plasma jets compresses the target plasma nearly adiabatically down to about 1 cm. The plasma density increases by 1000-fold. Its temperature increases by a 100-fold. Fusion reactions occur.

Figure 1. Kinetic energy is accumulatedin the plasma gun slowly (> 5 _s) and over a large
distance (~ 1 m), but deposited in a short time (< 0.1 _s) and smaller special extent (< 0.01 m), resulting in 4 orders of amplification in power density. In this paper, an experiment (PLX) to explore the physics of forming a 2-D plasma liner (shell) by merging plasma jets is described. The experiment complements the experimental investigation being led by Los Alamos National Laboratory for demonstrating and establishing the underlying physics principles of MTF. Successful completion of PLX and LANL MTF Concept Exploration Experiment will provide the necessary scientific data for further evaluation of the physics feasibility and the potential of MTF for practical energy and propulsion applications.

2. Experimental Goals and Parameters

The immediate physics issue concerning plasma-jets driven MTF (PJETS-MTF) is whether a plasma liner can be formed by merging plasma jets. The objective of the Plasma Liner Physics Exploratory Experiment (PLX) is therefore to perform experiments to study the dynamics of merging an array of plasma jets to form a plasma liner, and the implosion of a magnetized target plasma by the plasma liner. We now discuss the considerations leading to the quantitative selection of the experimental parameters for PLX.

To keep the experiment as simple as possible, the _'mqf,_ r
dimensions requiring a far _'_ number of plasma

physics of the jets merging guns and diagnostics than

is studied in for producing

two a 3-D

shell. A suite of first-generation computer codes on plasma liner formation can be developed and

validated against the experimental results. The codes could then be used to design a follow-on

experiment of greater complexity that would demonstrate the 3-D implosion of a magnetized target

by a 3-D liner. In PLX, a simpler experiment, using an array of 12 plasma guns arranged in a circle

to form a converging cylindrical plasma shell is proposed (Figure 2).

Figure 2. The Plasma Liner Physics Exploratory Experiment (PLX), consisting of merging 12 plasma jets launched by 12 coaxial plasma guns.

The principal objective of the PLX experiment is to pave the way for an experiment to demonstrate

the physics feasibility of the plasma-jets driven MTF approach. The parameters for PLX should therefore be carefully chosen so as to enable the Physics Feasibility Experiment (PFX) experiment.

Quantitatively, PFX should develop the physics and engineering database to enable the design of yet

a Proof-of-Principle

(POP) experiment for the PJETS-MTF concept at a considerably higher energy

level. The PoP experiment should at least demonstrate the attainment of a plasma temperature

exceeding 5 keV and a Lawson n rproduct within an order of magnitude required for fusion

breakeven. In turn, the Physics Feasibility Experiment PFX should demonstrate the attainment of

similar plasma temperature but with a Lawson product n c'two orders of magnitude less than in the

PoP experiment, that is, within three orders of magnitude of fusion breakeven.

The Lawson Criteria for Pulsed Fusion. For the fusion reactions to sustain itself, the rate at which the fusion energy is re-deposited in the burning fusing plasma must exceed the rate at which the plasma energy is lost to the surrounding. Thus,

cr nln2(ov)

3nkT _, > --

where n I , n 2 are the particle densities of the reacting species, (o'v) is the fusion reactivity, a is the fraction of the fusion energy re-deposited in the burning plasma, e s is the energy per fusion reaction, n is the total particle density, T is the plasma temperature, k is the Boltzmann's constant, and r I is the energy confinement time. For the D-T reaction,
D + T ----)4He (3.52 MeV) + n (14.06 MeV), (or) = 1.1×10-=m3s -1 @ T = 10 keV and assuming a 50% re-deposition of the o_-particle energy, the above condition reduces to,

n't% > 12kT =6× 10 2o s.m -3, 2 tl o =n T = --1n
Thus, the PFX experiment should aim at demonstrating the feasibility of integrating the physics and engineering approach to attain a Lawson product of about 6 x 1017 s.m -3.
For the physics outcome of the Plasma Liner Exploratory experiment (PLX) to be meaningful, the experiment should exercise all the essential physics and component technologies at a level required for the PFX experiment. In particular, the plasma gun and the plasma jet used in PLX should meet all the requirements of the PFX experiment and should be demonstrated during the PLX phase of the program. A suite of theoretical and computational models are to be developed that can be validated against the experimental results, so that they can be used with a sufficient degree of confidence to extrapolate the experimental results to the parameter space required to design the PFX experiment.


3. The Physics and Technology Requirements
In order to define the experimental parameters for PLX, the technological and physics requirements for PFX need to be identified first. In PFX, an array of plasma guns, as many as 60 guns, arranged symmetrically over a spherical surface is envisaged, that will launch an ensemble of plasma jets converging towards the center of the sphere to form a 3-D imploding spherical plasma shell. We will now set out to determine the requirements for PFX. To allow for a modest degree of physics excursion and exploration, we will "over-design" the experimental system by a factor of two to four for most of the plasma parameters (temperature, Lawson's number, neutron yield). The starting point is to select the implosion trajectories and profile required for the experiment. For this purpose, we will make use of the 0-D theory developed by Thio (6_.
Following Thio, assume a plasma liner in the form of a spherical shell of finite thickness converging on a target plasma, also assumed to be spherical. As the plasma liner and the target plasma are initially relatively cold with relatively low sound speed, when they collide, shock waves are produced in both the target plasma and the liner. The shock in the target plasma converges spherically towards the center and is reflected near the center. In time, the reflected shock meets the radially converging contact surface giving rise to a second radially ingoing shock in the target which is again reflected near the center. The process is repeated until the implosion velocity falls below the speed of sound in the target, after which point the compression proceeds in a shockless fashion. When the radial momentum of the liner is totally dissipated, the target and the liner have reached their peak compression. By design, the first ingoing and reflected shocks in the target are strong. The passage of these two shocks, however, heats the target to a sufficiently high temperature that the subsequent reflected shocks are relatively weak and may be ignored in the consideration of the target compression during this phase. If the magnetic field in the plasma is sufficiently high to provide the

requireddegreeof magneto-thermailnsulation,thenthecompressionduring this phaseis nearly adiabatic. At peaktargetcompressionf,urtheradvanceby the liner is haltedby the immensepressuredeveloped in thetarget.A stagnatingshockpropagatesoutwardin the liner with a "piston" speedapproximately equalto the local inward flow speedbeforethe arrival of the stagnatingshock.Whenthis stagnating shockreachesthe outerboundaryof theliner, a rarefactionwavepropagatesbackwardstowardsthe center.Theconfinementtime for the targetplasmais approximatelythe transittime of the stagnation shockplus twice the transittime of the rarefactionwave. Baseduponthe abovescenario,the requiredjet velocity to obtaina given targettemperatureis estimatedasfollows. Firstly, we pick aninitial radius(rj) andfinal radius(r2) for the compact toroid.
Choosing r_ to be 8 cm, and r2 to be 1 cm appears to be a reasonable choice. This gives the overall radial compression (rl]r2) of 8. The first spherically converging shock and its first reflected shock from the center lead to a density compression by a factor of 32 (1°), and the corresponding radial compression by a factor of 3.1748. After these two shocks, the compression proceeds by a series of relatively weak shocks multiply reflected between the center of the target and the converging liner. The compression by this series of weak shocks needs to provide a radial compression factor of (r_/r2)/ 3.1748. The temperature of the target at peak compression, Tf, is related to its temperature T2s after the first two strong shocks (just before the compression by the series of weak shocks) as,

Tf = [(rl / r2 )/ 3.1748] 2


assuming that the compression is completely adiabatic due to the magneto-insulation

of the

magnetized target. T2s is the temperature of the target after the passage of the first spherically

converging shock and its reflected shock through the target, and is given by (6),


27 7// _


• l+Zi

where uc and mi are the contact surface velocity and the jet ion mass respectively. The contact

surface velocity is sufficiently closed to the jet velocity ut for the purpose of this scoping exercise.

Given the temperature Ts of the target at peak compression, the above expressions determine the

required jet velocity. Figure 3a graphs the required jet velocity vs the target temperature reached.

to be

The liner energy required depends on the degree of compression, the mass of the target plasma and the target containment time desired. Given the target radius at peak compression, the mass of the target plasma is determined by its density at peak compression. Attaining a target plasma density of 1025 ions per m 3 at peak compression appears to be a reasonable goal of the experiment. To attain the Lawson product n_of 6 x 10 ]7 s.m -3, the energy confinement time needs to be at least 60 ns. Assuming that the energy confinement time is of the same order of magnitude as the plasma containment time, this implies that the plasma needs to be contained for at least 60 ns. This determines the amount of liner energy required. Using a 0-D magnetized target plasma compression code (MTFPL0) developed based on the compression dynamics given in Thio (6), the liner energy required vs the confinement time is shown in Figure 3b. It is seen from Figure 3a and 3b that the experimental objectives may be achieved with a jet velocity in the vicinity of 200 km/s, and a total liner energy of about 0.4 MJ. The corresponding mass of the plasma liner is 20 mg. With 60 plasma guns, the mass of each plasma jet is 0.33 mg. The dynamic formation of a plasma liner from the merging of the jets has never been attempted before in the manner and of the scale envisaged here where the plasma jets are transported over a large distance (> 1 m), detached from the electrodes of the plasma guns, and in particular, for


producing plasma liner having the momentum flux density envisaged here. Encouraging results, however, were observed in an experiment conducted in the US Air Force Research Laboratory at Kirtland AFB in the late 1980's, in which a circular array of 12 and 24 radial electrodes were used to produce a hypercycloidal discharge ° 1_.The 12 and 24 discharges formed a cylindrical plasma that was seen to implode towards the center. The experiment was a follow-up on an earlier experiment at Sandia National Laboratory in which a cylindrical array of eight plasma gun discharges were operated (12_. The objectives of these experiments were somewhat different from the experiment we are proposing here. They were designed to investigate the feasibility of achieving dense plasma focus (DPF) using multiple plasma guns to form a hypercycloidal discharge instead of a single coaxial plasma gun (13). The objective was to get around the limitation of a single plasma gun of conventional dense plasma focus. The experiment proposed here is unique in terms of forming a plasma liner using detached plasma jets produced by pulsed plasma accelerators or Marshall guns.


file: quasi static model pfx 0.6

_- 300 E
"_ 250
> ,& -_ 200
rr 150

_v0. 4









Target Plasma Temperature (keV)

0.1 0







Confinement time (ps)

Figure 3. (a) Liner velocity vs. target temperature, Liner energy vs. target confinement time.

assuming a radial convergence

ratio of 8. (b)

ExperimentTargetPlasma JetsPlasma LinerTarget Plasma