Forming and Maintaining a Potential Well in a Quasispherical Magnetic Trap

Abstract

The formation and maintenance of an electrostatic po tential well by injecting electrons into a quasi spherical cusped magnetic confinement geometry is studied ex perimentally, as a function of plasma fill density and of the energy and current of the injected electrons. A model is developed to analyze the experiment. It is found that the potential is comparable to the energy of the injected electrons at low density, and decreases as an increasing density of cold plasma fills the device because of ionization or wall bombardment. Implications for fusion based on electrostatic/magnetic confinement are discussed.

I. Introduction

Presentday fusion research is based on two approaches.Magnetic fusion confines a hot dense Maxwellian plasmamagnetically, with only the more energetic parts of theion velocity distribution participating in the fusionprocess. Inertial confinement fusion deposits a largeamount of energy in the form of laser light or ionbeams on the surface of a small solid target, causing animploding compression wave that raises the densityenough to trigger a fusion reaction. However, a thirdpossibility has long been suggested,1,2 though not muchstudied, namely, fusion produced by a cloud of converging ions, dense only near the center of a sphere, confinedby electrostatic potentials produced by grids, and havinga velocity distribution far from thermal equilibrium,being instead peaked near the energy at which the fusion cross sections are maximum.

An approach to fusion has been proposed by Bussard,3 ,4which keeps the advantages of convergent ions and electrostatic confinement without the disadvantages ofwires imbedded in the plasma. The idea is that in aplasma with a slight excess of electrons, a quasisphericalcusped magnetic field, Figure 1, would confine the electrons, while the electrostatic potential from the electronexcess would confine the ions, and accelerate them to adense focus at the center, where the probability of fusion would be high.4,5 The magnetic field can be formedby a set of highorder polyhedral windings that producea quasispherical array of point cusps,6 in a magneticgeometry called a Polywell. The physics of this idea hasbeen discussed in detail elsewhere,4,5 but clearly a centralfeature is the need to form and maintain an excess ofelectrons sucient to provide a substantial electrostaticpotential. Injection from highenergy electron gunsseems the only practical way to achieve this.

Recently an experiment was constructed to test someelements of this approach to fusion. The research activities included detailed studies on the injection and trapping of highenergy electrons in a Polywell magneticfield, both with and without a background plasma. Byvarying the parameters of the electron guns and thebackground plasma, information was obtained on manyproperties of the system, including plasma confinement,recycling of plasma from the walls, and breakdown of aneutral fill gas. Most important, however, was the information about the properties of the potential wellformed by electron injection, including its depth, radialprofile, time history, and dependence on system parameters. In this paper we describe these measurements, alongwith theoretical models, which help understand them.

In Section II we briefly describe only the aspects of theexperiment and diagnostics relevant to the present paper. In Section III we describe the formation of a potential well when electrons are injected into vacuum. InSection IV we describe and analyze experiments inwhich electrons were injected into a background prefillgas, and the potential measured, for various. values of filldensity and electron gun properties. In Section V wediscuss the results, as well as the implications of theseexperiments for the Polywell fusion scheme. In the Appendix we describe the formation and decay of a cooldense plasma in the Polywell produced by radio frequency RF ionization of a prefill neutral gas; this studyis directly relevant to the work discussed in Section IV,because it develops and benchmarks a model that reproduces experimental results on breakdown and confinement. This model can then be used with some confidence in the electron injection experiment.

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II. The HEPS Experiment

The HighEnergy Power Source HEPS experimentconstructed at Directed Technologies IncorporatedDTI used a motor generator set designed to provide inexcess of 4000 Amp at 4 kV to six seriesconnectedfield coils in approximately 225 ms, with 8 MJ of storedenergy, to produce the Polywell magnetic field6 shown incross section in Figure 1. This magnetic field has thesame structure whether viewed in the xy, yz, or xzplane, with the plane passing through x=y=z=0.

Electrons were injected into three of the magnetic cuspthroats, from electron guns capable of operating in therange 510 kV and 515 Amp. In these guns, electronswere emitted from a cathode, accelerated through ananode structure and allowed to pass through a drift tuberegion into the tank. Particle simulations and particleincell PIC codes7 showed that electrons must be injected along field cusp lines in order to access the centralvolume of the magnetic well.

The electron beam power supplies could produce 20Amp at 20 kV for a maximum 25 ms pulse with a minimum current droop <10 for each of three electronguns. The pulse width and charging voltage were variable, the rise time for the system was less than 30 μs,and the size of the extracted electron beam was 2 cm indiameter.

The parameters of the experiment are given in Table 1.In some experiments the electrons were injected into avacuum; in others the device was prefilled with a neutralgas or a plasma. In the prefill case, the neutral gas background was introduced using a system of piezoelectricpu valves prior to electron injection. A 10 kW, 2.45GHz RF source was then used to break down the neutral gas background.

The diagnostics relevant to the present paper included aprobe or set of probes inserted into the plasma to measure the potential relative to the wall. This diagnosticconsisted of a capacitivedivider potential probe8 whichsampled the potential at 54 radial positions. In the standard operating regime, the confining field was 1.5 kG atthe major point cusps, and the probe was inserted at themidplane 10° o the cusp axis Figure 1. The probemeasured true space potential to within 0.5T.

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A second diagnostic was a 94 GHz microwave interferometer. This system is of the MachZender design, inwhich the probe beam is split, undergoes one passthrough the plasma, and is recombined on the other sideof the tank. Four chords were employed at 0, 6, 13, and28 cm from the tank center. With a path length of 2 m,the system resolution was 5 x 109 cm3.

A third diagnostic was a Langmuir probe diameter 2mm, used to estimate the electron density. This diagnostic was used because in many of the experiments, theplasma density was below the resolution of the interferometer. The probe was mounted on a flexible bellows,which made it possible to place the probe tip at any radius in the chamber; it was inserted at the midplane 10° off the cusp axis, as was the potential probe describedabove. An adjustable bias 100 to + 100 V was appliedto the probe tip, and the current drawn by the probewas measured as a voltage drop across an 18  resistorconnected to ground.

Initial tests with the Langmuir probe were performedwith an electron cyclotron resonance ECR producedplasma to verify its correct operation. The probe biaswas varied on each ECR shot to obtain a typical Langmuir probe IV characteristic T = 1215 eV for theECR plasma. The electron saturation current was usedto determine the plasma density; the calibration of theLangmuir probe was obtained by measuring the plasmadensity with the microwave interferometer and the electron saturation current on the same shot. The calibration obtained was consistent within 50 with thatexpected using simple Langmuir probe theory neglecting B fields.

In some data runs, we utilized the probe to determinethe plasma density existing in the vessel prior to thefiring of the e guns, especially in the cases where thedensity was below the resolution of the interferometer.Once the e guns are fired, the highenergy, nonMaxwellian electrons prevent a simple interpretation ofthe signals obtained to infer density or the temperature.However, the probe signal can still be used in a semiquantitative fashion by subtracting the highenergy electron current flux to the probe, determined from the observed electron gun current, to estimate the saturationelectron current from the background plasma.

Finally, an energy analyzer was used to obtain at leastgrossly, the energy distribution of the higherenergyelectrons in the system. This diagnostic, placed at a cuspat the bottom of the vacuum vessel, included a pair ofgrounded grids, an electron repeller grid that can be biased from 0 to 15 kV, an ion repeller grid that can bebiased from 0 to + 15 kV, a secondary electron grid thatis biased at 30 V, and a collector plate.

The intent of the experiments described here was firstto demonstrate that an electrostatic potential well couldbe formed and maintained, both in a vacuum and in asystem with background plasma, and second to see if thecharacteristics of the potential in various ranges of gunenergy and current and various prefill densities wereunderstandable on the basis of straightforward classicalmodels. In other words, we asked whether there wereany obvious anomalies in this portion of the Polywellfusion scenario. The results described in the next section, along with the experiments described in the Appendix, lead us to conclude that potential well formationin the Polywell follows a predictable and understandablepath.

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