High-Energy Electron Confinement in a Magnetic Cusp Configuration

Abstract

We report experimental results validating the concept that plasma confinement is enhanced in a magnetic cusp configuration when β (plasma pressure/magnetic field pressure) is of order unity. This enhancement is required for a fusion power reactor based on cusp confinement to be feasible. The magnetic cusp configuration possesses a critical advantage: the plasma is stable to large scale perturbations. However, early work indicated that plasma loss rates in a reactor based on a cusp configuration were too large for net power production. Grad and others theorized that at high β a sharp boundary would form between the plasma and the magnetic field, leading to substantially smaller loss rates. While not able to confirm the details of Grad’s work, the current experiment does validate, for the first time, the conjecture that confinement is substantially improved at high β. This represents critical progress toward an understanding of the plasma dynamics in a high-β cusp system. We hope that these results will stimulate a renewed interest in the cusp configuration as a fusion confinement candidate. In addition, the enhanced high-energy electron confinement resolves a key impediment to progress of the Polywell fusion concept, which combines a high-β cusp configuration with electrostatic fusion for a compact, power-producing nuclear fusion reactor.

I. BACKGROUND

The use of magnetic fields to confine high-temperatureplasmas has been one of the main pathways pursued incontrolled thermonuclear fusion research since the 1950s.Several magnetic field configurations, such as magneticpinch, stellarator, magnetic mirror, and tokamak, have beenexplored to achieve net power generation from fusionreactions [1–3]. However, one of the critical technicalchallenges related to magnetically confined fusion devicesis the plasma instability inside the confining magneticfields. For example, magnetohydrodynamic instabilitiesdriven by plasma current or plasma pressure, such as kinkand Rayleigh-Taylor instabilities, can abruptly disrupt theplasma confinement by tearing apart confining magneticfields and expelling the plasma. Such plasma instabilities limit the maximum operating plasma current or pressure inthe device and increase the reactor size required to achievenet fusion power. Moreover, a large engineering safetymargin is typically required to prevent reactor failure in the event of a major disruption, increasing engineering com-plexities and reactor cost.

In comparison, the magnetic cusp configuration providesexcellent macroscopic plasma stability due to the convexmagnetic field curvature towards the confined plasma systemin the center, as shown in Fig. 1(a) [1,2,4]. Experiments onthe cusp field configuration have confirmed the stability property, even at very high plasma pressures up to β 1⁄4 1[5,6]. Plasma beta β is defined as the ratio of plasma pressureto confining magnetic field pressure, β 1⁄4 Pplasma=ðB2=2μ0Þ,where Pplasma is the plasma pressure, μ0 is the magneticpermeability, and B is the magnetic flux density. In a cuspconfiguration, the local value of β varies from zero where theplasma pressure is low, to infinity at the center where there isa finite plasma pressure with a zero magnetic field. When asingle value of β is given for the entire volume in this paper,it refers to the average plasma pressure inside the cuspsystem (near the center) normalized to the magnetic fieldpressure at the center of one of the magnet coils. Since thefusion power output scales as β2 for a given magnetic field,high-β operation is advantageous for a compact economicalfusion reactor. In contrast, the design parameter for theInternational Thermonuclear Experimental Reactor (ITER),a proposed tokamak device to achieve a net fusion poweroutput, is β ≈ 0.03 [7].

Substantial theoretical and experimental efforts havebeen devoted to investigating the magnetic cusp configu-ration [1,3,4]. Initial results, however, showed poor plasmaconfinement [1]. This was thought to be related to the openmagnetic field structure and rapid mirrorlike plasma loss ina low-β cusp. Grad and others predicted theoretically thatthe plasma confinement properties of the cusp configura-tion would be greatly enhanced if the magnetic fieldexhibits a sharp boundary separating the field-free high-β plasmas and the vacuum region with magnetic fields, asshown in Fig. 1(b) [1,8]. This change in magnetic fieldstructure is driven by plasma diamagnetism, thus propor-tional to β. Figure 1(b) shows schematically a cuspmagnetic configuration at β 1⁄4 1. Equation (1) describesthe theoretically estimated plasma loss rate for the cuspsystem in Fig. 1(b) [8]. The physical idea behind Eq. (1) isas follows: At high β, plasma approaching this sharptransition layer reflects back into the confined volumedue to the discontinuity in the magnetic field. Eventually,however, a plasma particle after many reflections will movealmost exactly in the direction of the cusp opening and willbe lost. Grad conjectured that this loss hole will have aradius equal to the electron gyroradius, as shown in Eq. (1).By contrast, when β is small in the cusp, the transitionregion is the size of the confined volume, and plasmaapproaching the boundary attaches to field lines andstreams out the cusp. This loss rate is related to the plasmaloss rate in a magnetic mirror and is much larger than therate given in Eq. (1) [9].

Equation (1) shows the electron and ion loss rate for asingle cusp with high-β plasma,

where I is the loss current, e is the electron charge, n is thedensity, v is the velocity, rgyro is the local gyroradius at the cusp location, and subscripts e and i denote electron andion species, respectively.

Though several experiments were constructed to validatethis conjecture, two critical issues limited their efforts[5,6,10–12]. The first issue was the engineering andtechnical challenge related to initially forming a high-βplasma, where a required initial injection power is onthe order of 100 MW or more. The second issue was thetheoretical and experimental difficulty in determining theplasma loss rate in a high-β plasma state. It was acceptedthat if the loss rate is determined by the ion gyroradius, itwould be unacceptably large for a fusion power reactor.Experiments seemed to indicate that the ion gyroradius didindeed dominate the loss rate [11], though another worksuggested that a hybrid radius between electron and iongyroradius gives the correct loss rate [12]. Because of theseproblems, the concept of a fusion power reactor based on acusp magnetic field was largely abandoned, until a newidea, discussed in the next section, was proposed thatretains the advantages of cusp confinement but removes theissue of the ion gyroradius dominating the loss rates.