Plasma Diagnostics for Tokamaks and Stellarators. "Plasma Diagnostics for Tokamaks and Stellarators
Total Page:16
File Type:pdf, Size:1020Kb
739 ISSN 0214-087X PLASMA DIAGNOSTICS FOR TOKAMAKS AND STELLARATORS Proceedings of íhe IV Course and Workshop on IVIagnetie Confinemení Fusión. UIMP Saníander (Spain), June 1992. Stott, P.E. Sánchezr J. (Editors) CENTRO DE INVESTIGACIONES ENERGÉTICAS, MEDIOAMBIENTALES Y TECNOLÓGICAS MADRID, 1994 CLASIFICACIÓN DOE Y DESCRIPTORES: 700320 PLASMA DIAGNOSTICS TOKAMAK DEVICES SPECTROSCOPY LNAGMUIR PROBÉ MICROWAVE SPECTRA EDGE LOCALIZED MODES STELLERATORS Toda correspondencia en relación con este trabajo debe dirigirse al Servicio de Información y Documentación, Centro de Investigaciones Energéticas, Medioam- bientales y Tecnológicas, Ciudad Universitaria, 28040-MADRID, ESPAÑA. Las solicitudes de ejemplares deben dirigirse a este mismo Servicio. Los descriptores se han seleccionado del Thesauro del DOE para describir las materias que contiene este informe con vistas a su recuperación. La catalogación se ha hecho utilizando el documento DOE/TIC-4602 (Rev. 1) Descriptive Cataloguing On- Line, y la clasificación de acuerdo con el documento DOE/TIC.4584-R7 Subject Cate- gories and Scope publicados por el Office of Scientific and Technical Information del Departamento de Energía de los Estados Unidos. Se autoriza la reproducción de los resúmenes analíticos que aparecen en esta publicación. Este trabajo se ha recibido para su impresión en Julio de 1993. Depósito Legal n? M-15175-1994 ISBN 84-7834-242-7 ISSN 0214-087-X ÑIPO 238-94-026-2 IMPRIME CIEMAT INDEX External Magnetic Diagnostics 1 I.H. Hutchinson Internal Magnetic Field Measurements 13 H. Soltwisch Magnetic Surfaces Measurements in Stellarators 30 E. Ascasibar Electric Probes in Magnetized and Flowing Plasmas 43 I.H. Hutchinson Interferometry and Polarimetry with High Spatial Resolution 55 A.J.H. Donné Microwave Reflectometry 76 J. Sánchez Reflectometry for Density Profile Studies 90 M.E. Manso Electron Cyclotron Emission and Absorption 112 I.H. Hutchinson Lecture on Thomson Scattering 125 T.N. Carlstrom Spectroscopic Studies of Impurity Densities and Impurity Transport 137 K. Behringer Charge-Exchange Spectroscopy in Fusión Plasmas 167 R.C. Isler Láser Induced fluorescence and Its Applications to Fusión Plasma Diagnosis 190 F.L. Tabarés Edge Turbulence Diagnostics 210 C. Hidalgo Fluctuation Measurements by IR Coherent Scattering 216 C. Laviron Application of FIR Collective Scattering to Investígations of Tokamak Microturbulence 225 D.L. Brower, C.L. Rettig, W.A. Peebles, K.H. Burrell, E.J. Doyle, R.J. Groebner, N.C. Luhmann, Jr. Extraordinary Mode Scattering or Scattering when the Incident Wave is near the Electron Cyclotron Frequency 263 N. Bretz The RTP Interferometer and its Application to Pellet Injection 300 J.H. Rommers, A.C.A.P. van Lammeren, F.W. Bliek, A.J.H. Donné RTP Team Technical Aspects of a Multichannel Pulsed Radar Reflectometer .... 306 S.H. Heijnen, C.A.J. Hugenholtz, M.J. van de Pol Amplitude Modulation Reflectometry for TJ-I Tokamak 312 E. de la Luna, V. Zhuravlev, B. Brañas, T. Estrada, J. Sánchez Development of a New ECA Sustem for RTP 317 J.F.M. van Gelder, M. Verreck, A.J.H. Donné EXTERNAL MAGNETIC DIAGNOSTICS I. H. Hutchinson Plasma Fusión Center & Department of Nuclear Engineenng, Massachusetts Institute of Technology Cambridge, Massachusetts, U.S.A. - i - External Magnetic Diagnostics In very many plasma experiments the main parameters of the experiment consist of the magnitude of currents and magnetic and electric fields inside and outside the plasma volume. Reliable measurement of these parameters is basic to performing and understanding the experiments. Moreover, in many cases, measurements of these global quantities can give considerable information about the microscopic properties of the plasma such as temperature, density, and composition. Magnetic diagnostics may not seem quite so exciting or to involve such interesting áreas of physics as the more exotic techniques, but there is little doubt that they are extremely productive and practical in routine use. 1 Magnetic Field Measurement Techniques The simplest way to measure the magnetic field in the vicinity of a point in space is to use a small coil of wire. Such a magnetic coil, illustrated in Fig. 1, may be considered the archtype of magnetic measurements. In a uniform magnetic field, varying with time B(t), the voltage induced in the coil is V^NAB , (1) where N is the number of turns in the coil of área A and the dot denotes time derivative. As indicated in the figure, because one is normally interested in B rather than B, an analog integrating circuit, such as the (somewhat schematic) one shown, is generally used to obtain a signal proportional to the field £ • where RC is the time constant of the integrator. Coil Integrator Figure 1: Typical magnetic coil and integrating circuit. - 2 - Many different kinds of magnetic coil configurations can be used. One which is very widely used is the Rogowski coil. This is a solenoidal coil whose ends are brought around together to form a torus as illustrated in Fig. 2. Consider a coil of uniform cross sectional área A, with constant turns per unit length n. Provided the magnetic field varíes little over one turn spacing, that is, if Figure 2: The Rogowski coil Figure 3: Equivalent geometry for the integral form of flux through a Rogwoski coil. \VB\/B«n , (3) the total flux linkage by the coil can be written as an integral rather than a sum over individual turns: $ = n <j>I í dAdA B • di (4) Ji JA where di is the line element along the solenoidal axis as illustrated in Fig. 3. Note that it is important to have the return wire back down the coil as shown in Fig. 2 or else to "back wind" the coil; otherwise, Eq. (4) also includes a term arising from the flux passing through the torus center. Now we note that the order of integration may be changed in Eq. (4) and that Ampere's law is quite generally B • di = (5) where I is the total current encircled by / and ¡i is the magnetic permeability of the médium in the solenoid. Thus $ = nAfxI (6) and the voltage out of the Rogowski coil is V = $ = nAfií , (7) which again is usually integrated electronically to give a signal proportional to I. — 3 The Rogowski coil thus provides a direct measurement of the total current flowing through its center. Note particularly that it is independent of the distribution of that current within the loop provided that Eq. (3) is satisfied. This principie is used in many different types of electrical circuits since it has the merit of requiring no circuit contact at all with the current being measured. The typical situation in plasma diagnostics in which it is used is to measure the total current flowing in the plasma, particularly for toroidal plasmas such as tokamak or pinch. For this purpose the Rogowski coil links the toroidal plasma as illustrated in Fig. 4. Transformer core Rogowski Voltage coi i loop Figure 4: Typical use of a Rogowski coil and a voltage loop to measure current and voltage in a toroidal plasma. 2 Global Measurements In a toroidal experiment the plasma current is driven by a voltage induced by transformer action, the plasma being the secondary. The toroidal loop voltage is usually measured by a so-called voltage loop, which is simply a single wire encircling the machine in the toroidal direction as illustrated in Fig. 4. If the plasma current is not varying with time, then the resistance of the plasma is evidently V¿//¿, where V¿ and 1$ are the toroidal loop voltage and plasma current, respectively. The resistance, Rp, of a toroidal plasma of major and minor radius R and a, respectively, 2 is related to its mean conductivity via a = 27ri2/7ra i2p, if a is uniform. If cr is not uniform but information about its profile shape is available, the resistance still provides a measure of its absolute magnitude. The usefulness of having a measurement of a, apart from determining the ohmic heating power density, is that it gives us an estímate of the electrón temperature. This estímate is based on the equation for the conductivity of a fully ionized plasma, T3/2 4 •Le a = 1.9 x 10 (8) where Te is the electrón temperature in electrón volts, Za is the resistance anomaly determined by the ion charge, and lnA is the Coulomb logarithm. - 4 - It is important to remark that Za is not just the quantity Ze// = Ylj njZ? /ne. However, an approximate relationship exists between them: Za ~ 0.65Ze// + 0.35 . (9) The electrón temperature deduced from Eq.(8) using Za = 1 (and an appropriate ínA, usually ~ 15) is called the conductivity temperature. It is usually a rather poor quantitative estímate of Te because of uncertainties in Ze/f and also because, in a torus, trapped particle effects can decrease the conductivity by a factor up to ~ [1 — y/(2r/R)) [1]. Nevertheless, the conductivity temperature is often a very useful first estimate because it is so easy to obtain. Externa! magnetic measurements are used routinely to give important information also about the plasma pressure. The basis of these diagnostics is that the plasma is in MHD equilibrium, where the plasma kinetic pressure is balanced by magnetic pressure. The mean plasma pressure < p > can be deduced from the "diamagnetic effect." The measurement in a toroidal plasma consists of measuring the mean toroidal field < B^ > using a flux loop (Fig. 5) and the toroidal field outside the plasma, B^a. It can then be shown [2] that the poloidal beta is approximately: 2fi<p> 2B (B -<B t >) ¡í>a 4>a < > (10) B¡ + Bl where Bga is the poloidal field at r = a. This measurement is hard to perform in tokamaks because it requires measurement of the small difference B<f,a — < B<j, > to an accuracy of order 4 10~ x B,pa.