Energy gain calculations in Penning fusion systems using a bounce-averaged Fokker–Planck model

Abstract

In spherical Penning fusion devices, a spherical cloud of electrons, confined in a Penning-like trap, creates the ion-confining electrostatic well. Fusion energy gains for these systems have been calculated in optimistic conditions ͑i.e., spherically uniform electrostatic well, no collisional ion-electron interactions, single ion species͒ using a bounce-averaged Fokker-Planck ͑BAFP͒ model. Results show that steady-state distributions in which the Maxwellian ion population is dominant correspond to lowest ion recirculation powers ͑and hence highest fusion energy gains͒. It is also shown that realistic parabolic-like wells result in better energy gains than square wells, particularly at large well depths (Ͼ100 kV). Operating regimes with fusion power to ion input power ratios ͑Q-value͒ Ͼ100 have been identified. The effect of electron losses on the Q-value has been addressed heuristically using a semianalytic model, indicating that large Q-values are still possible provided that electron particle losses are kept small and well depths are large.

Oscillating ions under Inertial Electrostatic Confinement (IEC) based on nanosecond vacuum discharge

“…therein), but due to different reasons, including a rather low value for efficiency, Q = E fusion / E input ∼ 10 −8 or even less, this concept regarding fusion was not developed properly. Just a couple of decades ago, interest in the IEC, mainly in a simple source of neutrons, was renewed . Nowadays, a broad spectrum of research findings on electrostatic confinement fusion is usually presented at the regular US–Japan workshops on the IEC (see, e.g., ref.…”

“…Thus, it could take more energy to maintain the non‐thermal distributions than what the device produces in fusion power. More complete theoretical studies (than the initial ones based on the simple analytical models ) have indicated that, if the ion distributions are close enough to thermal ones, net energy gains are possible, although the fusion power densities are small . Oscillating plasmas close to thermal equilibrium were suggested as a possible fusion scheme in the theory .…”

“…A tiny oscillating ion cloud, referred to as the periodically oscillating plasma sphere, or POPS, may undergo a self‐similar collapse in a harmonic‐oscillator potential formed by uniform electron background and could achieve the compressions and temperatures needed for fusion. Theoretical projections have indicated that such a scheme might be highly effective and may result in net fusion energy gain even for an advanced fuel such as DD . However, in spite of demonstrations of the oscillating plasma, until now, the POPS scheme has been studied much better in theory than experimentally …”

Space charge neutralization in inertial electrostatic confinement plasmas

“…11,12 However, these studies have several approximations, and a more complete study using a bounce averaged Fokker-Planck model indicated that if the ion distributions are close enough to thermal, net energy gains are possible, although the fusion power densities are small. 13 The underlying problem is that for nonthermal systems, the Coulomb scattering cross sections are larger than the fusion cross sections. Thus, it can take more energy to maintain the nonthermal distributions than the device produces in fusion power.…”

Stability of thermal ions confined by rigid-rotor electron clouds in Penning fusion systems

“…͑3͒-͑5͒, we have taken into account that, in the ion bounce time scale b ϳa/v i ͑with a the characteristic system size and v i ϳͱk B T/m i the ion characteristic thermal speed͒, ions are unmagnetized, adiabatic ͑because ie ӷ b , 9 where ie is the ion-electron collision time͒, and inviscid ͑because ii ӷ b , 9 where ii is the ion-ion collision time͒. In Eqs.…”