Electrons In Tokamak Research Articles

Effect of ripple on runaway electrons in tokamaks

A model of runaway electron generation and orbit predictions is described and applied to the problem of determining the influence of magnetic field ripple on the radiation loss and energy limits of runaway electrons. In particular the prediction of orbits and energy limits for a proposed ITER design are discussed. It is found that a resonance between the electron gyrofrequency and the fundamental ripple frequency can lead to large synchrotron radiation losses and create an upper bound on runaway energy which is strongly dependent on the pitch angle. Interactions with the second harmonic of the ripple field are very sensitive to the ripple amplitude and may lead to a further reduction in runaway energy. In ITER, this effect can limit the runaway energy to values of 270 MeV.

Improvement of Plasma Confinement during RF Current Drive in Tokamaks

It is shown that the E rf × B drift for resonant electrons in tokamaks does not cancel and forms an inward flux during rf heating with a travelling wave type spectrum when Dawson like treatment of Landau damping in the presence of the magnetic field is performed as an initial value problem, where E rf is rf electric field and B is the magnetic field. This effect could be the basis of the phenomenon that the plasma confinement is improved during low density lower-hybrid current drive in tokamaks.

A spatially scanning far-infrared interferometer for the measurement of tokamak electron density profiles

A far-infrared interferometer, illuminated with an optically pumped formic acid vapour laser, which uses a rotating mirror assembly spinning at high speed to scan the probing beam radially across a tokamak plasma, is described. This interferometer has been used on the University of Sydney's TORTUS tokamak, where the data recorded during each scan has been processed to yield radial electron density profiles of the 200 mm diameter plasma. The beam sweeps across the plasma in 1.0 ms, in which time the plasma electron density does not change significantly. Scans are obtained every 8.3 ms throughout the lifetime of the plasma. The phase shift due to the plasma is measured with an accuracy of +or-1/20th wavelength fringe shift, corresponding to an uncertainty in the electron density of +or-1*1018 m-3 and a spatial resolution of 20 mm for the 433 mu m wavelength used.

Extraordinary mode absorption at the electron cyclotron harmonic frequencies as a tokamak electron temperature diagnostic

An experimental study of extraordinary mode absorption at the semi-opaque second and third cyclotron harmonic frequencies has been performed on the Alcator C tokamak. A narrow beam of submillimetre laser radiation was used to illuminate the plasma in the horizontal plane, providing a continuous measurement of the onepass, quasi-perpendicular transmission. Experimental electron cyclotron absorption (ECA) data have been found to agree with theoretical results for lowest significant order in finite density and finite Larmor radius. The ECA data have been used together with data for the tokamak electron density and magnetic field to determine local electron temperatures in the range 75 ≤ Te(eV) ≤ 3300, with a spatial resolution of ≤ 1 cm. Transmission during lower hybrid radiofrequency (LHRF) heating and current drive remained unaffected by suprathermal electrons because of their low density and the relativistic downshift of the absorbing harmonics away from the laser frequency. Therefore, this permitted the ECA technique to be used to measure the bulk plasma temperature during LHRF heating. A density dependent non-resonant attenuation was observed which, when present, was taken into account in the data analysis.

Electron diffusion in tokamaks due to electromagnetic fluctuations

Calculations for the stochastic diffusion of electrons in Tokamaks due to a spectrum of electro-magnetic drift fluctuations are presented. The parametric dependence of the diffusion coefficient on the amplitude and phase velocity of the spectrum, and the bounce frequency for the electrons is studied. The wavenumber spectrum is taken to be a low order (5*5) randomly-phased, isotropic, monotonic spectrum extending from kperpendicular to min approximately= omega ci/cs to kperpendicular to max approximately=3 omega pe/c with different power laws of decrease phi k approximately= phi 1/km, 1<or=m<or=3. A nonlinear Ohm's law is derived for the self-consistent relation between the electrostatic and parallel vector potentials. The parallel structure of the fluctuations is taken to be such that k/sub ///nl nu e< omega k due to the nonlinear perpendicular motion of the electrons described in the nonlinear Ohm's law. The diffusion coefficient scales approximately as the neo-Alcator and Merezhkin-Mukhovatov empirical formulas for plasma densities below a critical density.

Kinetic theory of anomalous transport processes in tokamaks

A kinetic equation is derived which describes the behaviour of electrons in tokamaks in the presence of intensive low frequency fluctuations of electric and magnetic fields. For ‘collision integrals’ of particles with fluctuations some expressions of a specific character are found. A complete system of hydrodynamic equations describing the behaviour of both the electron component and the quasi-neutral plasma as a whole is obtained. Fluctuations are shown to lead not only to anomalous transport processes, but also to new essential terms in the equations for energy and momentum transport. – Fluctuations have a particularly strong effect on superthermal and runaway electrons. The distribution of runaway electrons in energy and in the tokamak cross-section is found, and the flux of accelerated limiter reaching relativistic electrons is determined. These results agree qualitatively with observations. – The essential difference in the dynamics of runaway electrons for ‘collisions’ with electrostatic and magnetic fluctuations is demonstrated. A quantitative analysis of these data can be used for evaluating magnetic fluctuations in tokamaks.

A far-infrared Michelson interferometer for Tokamak electron density measurements using computer-generated reference fringes

A simple far-infrared interferometer which uses the 394 mu m laser line from optically-pumped formic acid vapour to measure tokamak electron density is described. This interferometer is unusual in requiring only one detector and a single probing beam since reference fringes during the plasma shot are obtained by computer interpolation between the fringes observed immediately before and after the shot. Phase modulation is provided by a rotating mirror modulator. Electron density has been measured with a phase resolution corresponding to +or-1/20 wavelength fringe shift, which is equivalent to a central density resolution of +or-0.1*1019 m-3 for an assumed parabolic density distribution in a plasma of diameter of 0.2 m, and with a time resolution of 0.2 ms.

MEASURING ELECTRON CYCLOTRON RADIATION FROM PLASMAS BY MEANS OF CONFOCAL RESONANTOR

A method of measuring the electron cyclotron radiation from plasmas by using confocal resonant cavity and sweep frequency receiver is proposed. A radiation spectrum expression for a uniform plasma slab in the confocal resonant cavity has been derived. The analysis shows this method can independently measure TOKAMAK's electron temperature and its radial distribution. Furthermore, as a quasi-optical receiving system, it possesses high spatial resolution power.

Effects of discharge cleaning on the production of runaway electrons in TORTUS tokamak

Experimental results are presented on the production of runaway electrons as a function of wall cleanliness in the TORTUS tokamak. When the walls are clean, the production rate decreases as the filling pressure increases. When the walls are contaminated by oxygen, the production rate can increase when the filling pressure is increased, owing to the production of water vapour during tokamak discharges. These results resolve the differences reported in the literature on the production of runaways as a function of filling pressure. It is also observed that the runaway electron instability seen in other devices is suppressed when the walls are discharge-cleaned.

Numerical simulation of tokamak electron dynamics

In a tokamak, the electron distribution deviates from a Maxwellian because magnetically untrapped electrons run away parallel to the applied electric field. A new method for calculating the dynamics of the electron distribution is presented. This method is novel because it can treat systems with comparable numbers of trapped and untrapped electrons, and an electric field comparable with (but smaller than) the Dreicer field. The electron distribution function and the plasma resistivity are presented for representative values.

Electric field effects on relativistic charged particle motion in Tokamaks

The authors consider the relativistic guiding center motion of charged particles (charge e, rest mass m0) in magnetic fields consistent with toroidal Tokamak equilibrium. The particle acceleration due to the toroidal electric field-essential to Tokamak operation-is taken into account. For the case of weak acceleration (eU/m0C2<<1, where U is the loop voltage), the poloidal locus of charged particle motion is found to be an envelope of closed drift orbits which, in the case of large aspect-ratio, are characterized by adiabatic invariance of their cross-sectional area. This allows, in the absence of collisions, a complete description of the motion and confinement of runaway electrons in Tokamaks. For peaked current distributions and sufficiently high energies drift separatices exist. They are calculated and their relevance to charge particle confinement and injection is considered.

Kinetic theory of convective ripple transport in tokamaks

The ripple transport of fast (suprathermal) ions and electrons in tokamaks is investigated. This transport, which is due to the drift motion of particles blocked in the ripple of a magnetic field, is of the convective type for particles with an energy exceeding some value ℰd. For ions in real tokamaks, this energy region may be close to the bulk of ions having thermal energy. Kinetic equations for the particle distribution function are derived, the ripple drift motion through the magnetic surfaces being taken into account. In the low-energy (diffusive) limit, the results agree with the well-known ones. For more energetic particles convective transport dominates. In particular, a replacement, through the ripple channel, of fast electrons from the hot periphery is possible, resulting there in a considerable rise of the distribution function tail. The increase in the ripple depth from the chamber centre to the periphery is very important; it causes collisionless adiabatic capture of particles by ripples, which are held there, then drift and finally escape from the plasma. This process leads to the formation of a special type of trajectories (‘open’ trajectories) , which directly connect the chamber walls with the central position of the plasma column and may bring about considerable particle and energy losses. In addition, this phenomenon leads to a depletion of the particle distribution function.

Measurement of the spectrum of tokamak electron cyclotron emission on a submillisecond time-scale

An experiment is described in which the spectrum of electron cyclotron emission from a tokamak plasma is measured in a time interval of about 0.5 msec using a plasma-scanned Michelson interferometer. Results obtained from data taken during the tokamak current plateau, when the emission is known to remain relatively constant, are compared with those obtained using an established but slower (about 10msec) mechanically scanned interferometer. Good agreement is obtained. On the basis of this comparison we go on and make the first measurements of the emission spectrum during the early phase of the tokamak discharge and these measurements are also presented.

Kinetic theory of runaway production in toroidal magnetic devices

A kinetic equation is derived for fast electrons in toroidal, tokamak- or stellarator-type magnetic devices. It is of a different type for different groups of electrons, i.e. passing or trapped electrons, in a magnetic field. The solution of the kinetic equation is found, and analytic expressions for the electron distribution function are obtained for the case of an ideal (non-rippled) torus and an electric field weaker than the critical Dreicer field. The runaway flux of electrons is found. The case of a rippled torus is investigated by taking account of the vertical drift resulting in electrons blocked in the ripples being lost to the chamber walls. Considerable plasma loss is shown to be possible only for electrons of an energy exceeding some quantity ℰd, which depends on the magnetic field, the depth of the ripple, the plasma density, and the parameters of the device.

Drift-Modified Tearing Instabilities Due to Trapped Electrons

It is shown that the collisional detrapping of magnetically trapped electrons in tokamaks can excite drift tearing modes with high azimuthal mode numbers. For normal temperature gradients ($\frac{d\mathrm{ln}{T}_{e}}{d\mathrm{ln}n}&gt;0$), the modes are unstable in the collisional regime (${\ensuremath{\nu}}_{\mathrm{eff}}&gt;{\ensuremath{\omega}}_{^{*}e}$), but stable in the collisionless regime (${\ensuremath{\nu}}_{\mathrm{eff}}&lt;{\ensuremath{\omega}}_{^{*}e}$).

Nonlinear Evolution of Runaway-Electron Distribution and Time-Dependent Synchrotron Emission from Tokamaks

Stability of the runaway electrons in tokamaks is analyzed. The distinction between high-density and low-density operation of tokamak discharges is interpreted in terms of the stability condition obtained. In the unstable case, the temporal evolution of the distribution function of the runaway electrons is obtained by solving the quasilinear equation. Time-dependent synchrotron emission from the runaway electrons is calculated. (AIP)