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The m = 2 mode stability is investigated in the ISAR T1-B toroidal high-beta stellarator (major diameter 2.7 m, capacitor bank energy 0.5 or 1.5 MJ) for a great variety of plasma parameters using deuterium filling gas (0.5 < ω_L · τ_ii < 200; 0.1 < r_L/a < 0.35; ω_L = ion Larmor frequency; r_L = ion Larmor radius; a = plasma radius; τ_ii = ion self-collision time). The ion mass dependence was checked by a small number of discharges with hydrogen. For r_L/a < η_crit, η_crit = 0.14, fast-growing m = 2 modes were found, the limit η_crit being essentially independent of the collision frequency within the accessible range (2 ≲ ω_L · τ_ii ≲ 20). For r_L/a > 0.14 no fast-growing m = 2 modes were observed, the plasma lifetime being limited by a m = 1, k ≈ 0 mode. The normalized growth rate, = γ/(V_i/a) = 0.15 ± 0.05, (V_i = ion thermal speed) was about half the sharp boundary value and slightly higher than that calculated for a diffuse pressure profile. The experimentally determined minimum value of r_L/a, for which the m = 2 mode is stabilized, is by about a factor of three smaller than Freidberg's estimation using a sharp-boundary Vlasov model. Advanced calculations in a sharp boundary model by Lewis and Turner deviate in the critical limit only by a factor of about 1.5 and recent results using a diffuse pressure profile by Herrnegger and Schneider and by Freidberg and Hewett agree quite well with the experimental data.

The reaction p + ¹¹B → 3α + 8.7 MeV is evaluated as a potential fuel for a controlled thermonuclear fusion reactor. It is shown that successful fusion power from p-¹¹B is not to be expected in magnetic confinement devices because of very large synchrotron radiation losses. Laser fusion might be a more appropriate approach if it is proved feasible.

Magnetohydrodynamic (MHD) tokamak equilibria are found with values of β up to 20% and realistic MHD safety factor values (e.g. q(axis) = 1 and q(edge) = 4.8) for tokamaks with aspect ratio A = 4 and D-shaped cross-section. If such equilibria can be attained experimentally, they will be very attractive for decreasing the projected costs of tokamak power reactors. In the flux-conserving tokamak (FCT) model, where rapid heating is applied to an already relatively hot plasma, these high-β equilibria are achievable. The quasi-static evolution of FCT equilibria as β increases is studied. An operating window is found in the pressure profile width w_p at the half-height: for high β, the values of w_p lie between 0.40 and 0.55 times the minor plasma diameter. Within this window, plasma current and poloidal β increase with β. For fixed plasma boundary, significant poloidal surface currents are induced, but these can be eliminated by small increases in the plasma minor radius, the pressure profile width, or the vacuum toroidal field.

A straight, uniform-current, elliptic-cross-section plasma maintained in equilibrium by a quadrupole field is studied. Asymptotic analysis is used to show the existence of an 'infinity' of bifurcation points. Numerical investigation confirms the analysis and yields examples of m = 2 (elliptical), m = 3 ('pear-shaped'), and m = 4 configurations. Further analysis shows the possibility of multi-columnar equilibria. The role of constraints with respect to elliptic equilibria is discussed.

A computational study has been made of the energy amplification factor Q to be expected in a toroidally linked mirror (TLM) reactor, using the one-dimensional multi-species Fokker-Planck code ISOTIONS. Because of the uncertainty which exists over the effect of ambipolar electric fields on diffusional losses from TLM systems, two model loss terms have been considered. For each model, Q has been calculated for a range of values of the mirror ratio, the ion injection energy _inj, and the 'critical energy' _c, of TLM diffusion theory. For values of _c/_inj ∼ 0.5, Q is very significantly enhanced with respect to the value in a single mirror machine, even in the relatively pessimistic model.

The transport in tokamaks due to collisions between impurity ions in the Pfirsch-Schlüter regime and light ions is considered. The diffusion coefficients for the particles have a Pfirsch-Schlüter-like structure for all the regimes of light ions. They experience, however, a transition from a set of values (A) to a different set of values (B), when the quantity v²_thℓ τ_Dℓτ_Mℓ (qR)⁻² varies through a value of the order unity. (v_thℓ and τ_Dℓ, τ_Mℓ are the thermal velocity and the relaxation times for deflection and Maxwellization of light ions, respectively.) The values (A) (applicable, in particular, when the light ions are in the banana and plateau regimes) allow, in principle, plasma purification by the ion temperature gradient.

The MHD spectrum associated with small perturbations about an analytic equilibrium is determined for a configuration with magnetic flux surfaces which are nested similar elliptic cylinders generated by a uniform axial current. Since the system is periodic, it models the essential features of a toroid. Both analytic and numerical techniques are used to investigate many properties of the modes, including the continuous shear Alfvén and slow acoustic spectra as well as the discrete modes associated with fast magnetosonic waves, kinks, and instabilities where the interchange criterion is violated. In particular, the relationship between discrete and continuum modes is described both qualitatively and quantitatively, and it is shown how the unstable interchange modes emerge from the shear-Alfvén branch of the spectrum.

Theoretical and numerical studies of anomalous transport due to the lower-hybrid-drift instability show that this mode can cause significant diffusion in post-implosion theta pinches where T_i ≫ T_e and the electron drift velocity is below the ion thermal speed. Numerical results show that the diffusion scales with the simple diffusion velocity V_D ∼ (c²ν_an/ω²_pe) [∂ℓnB_z/∂x] = − (c²ν_anβ/2ω_pe²) [∂ℓnn/∂x], where ν_an is the anomalous collision frequency for the lower-hybrid-drift instability, estimated from quasilinear theory. (Here, B_z is the magnetic field, n is the density, and β = 8πnT_i/B_z² is the local value of beta.) Moreover, the time evolution of the sheath width in the numerical calculation agrees well with the simple theoretical estimate [L_n(t)/L_n(t=0)]⁴ = 1 + 4[V_D(t=0)/L_n(t = 0)]t, where L_n(t) is the density sheath width [L_n ≅ −(∂ℓnn/∂x)⁻¹]. This simple formula for lower-hybrid-drift sheath broadening is valid for 0.5 r_Li < L_n < 0.5 (m_i/m_e)^1/2r_Li, where r_Li is the ion Larmor radius.

Particle and heat diffusion fluxes due to toroidal drift of bananas in helical solenoids, i.e. solenoids wound around a circular torus, are discussed. Particle collision frequency ranges, in which the effective trapped-particle collision frequency is lower than the inverse trapped-particle period of oscillation between the magnetic mirrors, but higher than the frequency of banana precession around the magnetic axis, are considered. It is shown that for this regime the diffusion coefficients in helical solenoids may be greater than those in a three-turn stellarator, but smaller than those in stellarator-type traps with a helical magnetic axis produced by the magnetic fields of the helical windings.

A study of the trapped ion instability in the real geometry of the large tokamaks leads to the consideration of a new branch of that instability, driven by a resonance with the magnetic drift of the particles, both in collisional and non-collisional regimes.

During hard disruptions, dangerous overheating of the limiter can be avoided if it is protected by a dense, cold, high-Z plasma blanket - the "virtual limiter", as it has been termed throughout the present paper. The virtual limiter intercepts the particles escaping from the hot plasma core, and radiates away the absorbed energy as a flux of soft X-rays. The physics of such a process is investigated in the present paper, and specifications are derived for the achievement of effective protection.

The expansion of the ℓ = 2 stellarator magnetohydrostatic equilibrium around its circular magnetic axis is reconsidered. All parameters occurring up to third order in the distance from the magnetic axis are kept finite. Equilibrium and stability plasma β estimates are calculated in connection with a discussion of stagnation points occurring in the third-order flux surfaces. Results for the case without toroidal current are: irrespective of the five parameters describing this type of stellarator, there are universal bounds for the β estimates of 0.66% and 0.22% for the necessary and the sufficient stability criterion, respectively.

The main purpose of this second topical meeting, which was organized by the American Nuclear Society and its Richland Section and co-sponsored by the US Energy Research and Development Administration and the Electric Power Research Institute (EPRI), was to review and assess controlled nuclear fusion technological developments in the past two and a half years since the first topical meeting in San Diego in 1974. A total of 360 persons attended the second topical meeting of the ANS Controlled Nuclear Fusion Division, whose primary interest lies in the technology and engineering associated with fusion applications, mostly for power production. As regards attendance, the breakdown by organizational affiliation was as follows: US National laboratories 43%; industrial companies 33%; universities 10%; organisations outside the USA 6%; US government 4%; students 2% and utility companies 2%. At the first topical meeting in San Diego, where total attendance was somewhat higher, 27% of those attending were from industry and 20% from universities. The increase in interest by the private industrial sector in this second meeting is surely a healthy sign and presumably is a result of the increased design work that has taken place in the past couple of years.

This international symposium was organized by the Kernforschungsanlage, Jülich GmbH, co-sponsored by the Commission of European Communities (EURATOM) and attended by about 150 participants. Seventeen invited papers and about 69 contributed papers were presented, covering six topics.

One opportunity for exchanging information on Lasers, Plasma and Related Phenomena, such as Laser Compression for nuclear fusion or extremely high interaction intensities, has been the series of Workshop-Conferences organized at Rensselaer Polytechnic Institute beginning in 1969. The 4th meeting, 8–12 November, 1976, brought together more than 70 participants from 13 countries (Argentine, Australia, Brazil, Canada, England, France, Federal Republic of Germany, India, Israel, Italy, Japan, USA and the USSR), where 53 scientific papers were discussed under the sponsorship of RPI and ERDA.