Table of contents

Gyrokinetic theory is based on an asymptotic expansion in the small parameter , defined as the ratio of the gyroradius and the characteristic length of variation of the magnetic field. In this paper, this ordering is strictly implemented to compute the electrostatic gyrokinetic phase-space Lagrangian in general magnetic geometry to order ². In particular, a new expression for the complete second-order gyrokinetic Hamiltonian is provided, showing that in a rigorous treatment of gyrokinetic theory magnetic geometry and turbulence cannot be dealt with independently. The new phase-space gyrokinetic Lagrangian gives a Vlasov equation accurate to order ² and a Poisson equation accurate to order . The final expressions are explicit and can be implemented into any simulation without further computations.

Significant broadening of the energy spectrum of the products of nuclear reactions occurs in fusion plasmas. We provide a method for calculating the shape of this production spectrum for arbitrary plasma distribution functions. The method is exact and can be used for both isotropic and anisotropic distributions. We derive expressions for Maxwellian (both stationary and moving with a bulk fluid velocity), bi-Maxwellian and beam–target plasmas. The neutron spectrum produced by the D + D → He³ + n reaction is studied as an example. It is shown that the neutron spectrum produced from a Maxwellian plasma becomes asymmetric at high plasma temperatures with a long high-energy tail. The effect of bulk fluid velocity on the neutron spectrum is shown to be significant in some cases. In particular, the spectrum produced by an imploding shell has a much greater FWHM than the spectrum obtained from a stationary plasma. The spectrum produced by a beam–target interaction shows significant anisotropy in the high-energy tail as the viewing angle varies from perpendicular to parallel to the beam direction.

The nonlinear dynamics of electrostatic solitary waves in the form of localized modulated wavepackets is investigated from first principles. Electron-acoustic (EA) excitations are considered in a two-electron plasma, via a fluid formulation. The plasma, assumed to be collisionless and uniform (unmagnetized), is composed of two types of electrons (inertial cold electrons and inertialess kappa-distributed superthermal electrons) and stationary ions. By making use of a multiscale perturbation technique, a nonlinear Schrödinger equation is derived for the modulated envelope, relying on which the occurrence of modulational instability (MI) is investigated in detail. Stationary profile localized EA excitations may exist, in the form of bright solitons (envelope pulses) or dark envelopes (voids). The presence of superthermal electrons modifies the conditions for MI to occur, as well as the associated threshold and growth rate. The concentration of superthermal electrons (i.e., the deviation from a Maxwellian electron distribution) may control or even suppress MI. Furthermore, superthermality affects the characteristics of solitary envelope structures, both qualitatively (supporting one or the other type, for different κ) and quantitatively, changing their characteristics (width, amplitude). The stability of bright and dark-type nonlinear structures is confirmed by numerical simulations.

As a result of toroidal rotation, sequences of new global modes are predicted to arise in magnetically confined plasmas. The frequencies of these Alfvén modes lie inside gaps of the continuous magnetohydrodynamic (MHD) spectrum that are created or enlarged by toroidal flow. The numerically obtained results are compared with an analytical investigation, yielding a useful criterion for mode existence. Because of their low frequencies, these modes may be easily destabilized by energetic particles. Because of their sensitivity to the Mach number however, these modes can provide a valuable extension to MHD spectroscopy by giving information on the rotational velocity.

The intensity of emission lines in the ITER divertor plasma is synthesized using a model of the edge and scrape-off layer plasma. The intensity of hydrogen isotopes and impurities observed with the divertor central optical system of the Impurity Influx Monitor (Divertor) is estimated. In both inner and outer divertor plasmas, ionizing and recombining plasma components are observed for C I–III, and the recombining plasma component is dominant for C IV–V. Line-of-sight integrated spectra are synthesized in the wavelength range 200–1000 nm using photon emission coefficients. In order to evaluate the carbon-impurity influx, identifying the plasma component, i.e. an ionizing or recombining plasma component, is important.

We use the two-dimensional analysis code KUAD2 to simulate trajectories in an Inertial Electrostatic Confinement (IEC) device driven by a ring-shaped magnetron ion source (RS-MIS). This aims to maximize the path length λ_CX for ion-gas charge exchange by operating at just units of mPa D₂ gas pressures; however, under these conditions simulations reveal a surprisingly small path length for ion loss to the (Mo) cathode grid λ_grid ∼ 30 cm ≪ λ_CX. By developing an ad hoc model relating the time variation of cathode temperature and absorbed D₂ surface density, we use the simulated flux Γ_grid of ions striking the cathode grid to obtain the neutron production rate (NPR) arising from 'beam-grid' reactions. Results indicate that at units of mPa pressures, beam-grid NPR may dominate over the 'beam-gas' and 'beam-beam reactions,' providing a qualitative explanation for earlier experimental observations of time-varying NPR-dependence on cathode grid current and gas pressure.

The angular momentum conservation equation is considered for an electron gas, in the presence of Laguerre–Gaussian (LG) plasmons propagating along the z-axis. The LG plasmons carry a finite orbital angular momentum despite longitudinal nature, which can be partly transfered to the electrons. For short timescales, such that ion motion can be neglected, plasmons primarily interact with the electrons, creating an azimuthal electric field and generating an axial magnetic field. This effect can be called an inverse Faraday effect due to plasmons. Numerically, it is found that the magnitude of the magnetic field enhances with the plasmon density or with the energy of the electron plasma waves. A comparison of the magnitudes of the axial magnetic field is made for the inverse Faraday effect excited by both plasmons and transverse photons.

The ideal magnetohydrodynamic stability is investigated of localized interchange modes in a large-aspect ratio tokamak plasma. The resulting stability criterion includes the effects of toroidal rotation and rotation shear and contains various well-known limiting cases. The analysis allows for a general adiabatic index, resulting in a stabilizing contribution from the convective effect. A further stabilizing effect from rotation exists when the angular frequency squared decreases radially more rapidly than the density. Flow shear, however, also decreases the stabilizing effect of magnetic shear through the Kelvin–Helmholtz mechanism. Numerical simulations reveal the merits and limitations of the performed local analysis.

Axisymmetric plasma equilibria with toroidal flow are investigated using a two-fluid analysis, taking into account the presence of momentum and current drive, together with dissipative effects. The equilibria are described by a set of three equations describing the spatial variation of poloidal magnetic flux, plasma pressure and toroidal magnetic field. These equations indicate that magnetic flux surfaces do not in general rotate as rigid bodies, as required by ideal magnetohydrodynamics in the absence of momentum sources and poloidal flows. For specific momentum drive and damping scenarios, expressions are obtained giving the variation of density on flux surfaces and the dependence of toroidal rotation rate on temperature that can in principle be tested experimentally. A simple relationship between the loop voltage and plasma current in an inductive tokamak plasma with toroidal flow is also derived.

Inertial fusion energy (IFE) offers one possible route to commercial energy generation. In the proposed 'shock ignition' route to fusion, the target is compressed at a relatively low temperature and then ignited using high intensity laser irradiation which drives a strong converging shock into the centre of the fuel. With a series of idealized calculations we analyse the electron transport of energy into the target, which produces the pressure responsible for driving the shock. We show that transport in shock ignition lies near the boundary between ablative and heat front regimes. Moreover, simulations indicate that non-local effects are significant in the heat front regime and might lead to increased efficiency by driving the shock more effectively and reducing heat losses to the plasma corona.

This paper discusses the existence of solitary electromagnetic waves trapped in a self-generated Langmuir wave and embedded in an infinitely long circularly polarized electromagnetic wave propagating through a plasma. From a mathematical point of view they are exact solutions of the one-dimensional relativistic cold fluid plasma model with nonvanishing boundary conditions. Under the assumption of travelling wave solutions with velocity V and vector potential frequency ω, the fluid model is reduced to a Hamiltonian system. The solitary waves are homoclinic (grey solitons) or heteroclinic (dark solitons) orbits to fixed points. Using a dynamical systems description of the Hamiltonian system and a spectral method, we identify a large variety of solitary waves, including asymmetric ones, discuss their disappearance for certain parameter values and classify them according to (i) grey or dark character, (ii) the number of humps of the vector potential envelope and (iii) their symmetries. The solutions come in continuous families in the parametric V–ω plane and extend up to velocities that approach the speed of light. The stability of certain types of grey solitary waves is investigated with the aid of particle-in-cell simulations that demonstrate their propagation for a few tens of the inverse of the plasma frequency.

One-dimensional linear theory of radial correlation reflectometry (RCR) is developed. The dependence of scattering signal on the fluctuation wave number is carefully examined in the case of linear and arbitrary plasma density profiles. The behaviour of scattering efficiency is analysed and singularity saturation at a scale much lesser than the Airy scale is demonstrated. The expression for the RCR cross correlation function is derived and the possibility of turbulence wave number spectrum reconstruction based on the RCR data is shown.

The conditions for generating light ions (Li³⁺, Be⁴⁺, C⁶⁺ and Al¹³⁺) that have suitable energy deposition for the fast ignition of fusion targets via the interaction of an intense ultrashort pulse laser with thin targets (converters) are investigated theoretically. The laser and converter parameters are estimated assuming monoenergetic ions and a one-dimensional parallel plane geometry. Laser energy densities of 3–20 J µm⁻² focused onto a spot with radius 30–100 µm are required to attain the necessary kinetic energies of 10–50 MeV/nucleon, depending on the type of ion. Self-consistent two-dimensional relativistic particle-in-cell simulations show that light ions can be accelerated to the required conditions with a conversion efficiency of laser energy into ions of up to 25%. Using the output ion energy distribution function, a one-dimensional energy deposition model calculates the conversion efficiency of ion beam energy into the core of the DT fuel. We conclude that fast ignition driven by all light ions under consideration can potentially be used as an alternative to electrons and protons.

Carbon ions are used to heat the precompressed deuterium–tritium (DT) fuel in a cone-guided fast ignitor scheme with an areal mass density of about 2.6 g cm⁻². An ultra-intense laser pulse with a focal intensity of 1.45 × 10²² W cm⁻² accelerates the carbon ions to an energy of 450 MeV from a homogeneous layer of 0.2 g/cm³ density, which fills the head of the gold cone. Pellet ignition was observed in hybrid numerical simulations for a laser energy of about 65 kJ in a rectangular pulse of 4 ps duration. This corresponds to estimated overall efficiencies of more than 24% for ion acceleration and 17% for core heating. Reducing the laser intensity to the value 5 × 10²¹ W cm⁻², carbon ions with the energy of 175 MeV will be accelerated, and ignition occurred in hydrodynamic simulations for a laser energy of 115 kJ at a reduced heating efficiency of 6%. The comparison with ignition of a large-scale DT pellet, showing similar hydrodynamic characteristics and heated by in situ accelerated DT ions with 10 MeV mean energy, demonstrates the advantage of the carbon ion ignitor beam due to the more effective acceleration and expected higher directionality.