Special emphasis was given to the measurement of the complex charging impedance of the plasma. Special attention was paid to the measurement of the complex plasma charge impedance of the plasma at the cavity modes. The ratio of the real part of the plasma load impedance and the antenna resistance determines the efficiency of the wave generation in the tokamak at the cavity modes.
The estimated Q obtained from the density data is the cavity Q loaded by the antenna impedance and the r.f.
COLD PLASMA THEORY AND CIRCUIT MODELING OF THE CAVITY MODES 2.1 Theory for a Cold Uniform Cylindrical Plasma Cavity
The poloidal mode number, m, is the integer order of the Bessel function in the solution (2.1.2). They also calculated the damping due to the finite conductivity of the tokamak wall [4]. The fields in the cavity can be expanded in terms of the normal modes with the following coefficients: Eo= JE·E.{.
The solutions of the fields must satisfy both the Maxwell 1s equations and the boundary conditions.
Circuit Model of Toroidal Eigenmodes
GENERAL EXPERIMENTAL SETUP
A toroidal magnetic field is created by a current-carrying coil wound on the surface of the torus. The purpose of the ohmic heating coil is to produce a changing magnetic flux that connects the plasma, but not to have a field within the vacuum that disrupts the plasma confinement. The rotation angle 1(a) at the edge of the plasma. of toroidal current Conductor corresponds to toroidal current. 8 = the peloidal angle, and ¢ = the toroidal angle.
Second, the current will also heat the plasma through plasma resistance dissipation; hence the name, ohmic heating current. A side effect of discharge cleaning is that the plasma density drops very quickly after the initial rise in plasma density. To measure this voltage, a coiled wire is placed around the outside of the vacuum chamber in the direction of the plasma current.
Zeff is the effective charge of the plasma due to the high mass of impurities in the plasma [28]. One would also like to know the position of the plasma column relative to the wall of the vacuum chamber to keep the plasma properly centered. Therefore, the signal from the left half of the windings has opposite sign to the right half.
As the plasma moves to one side of the chamber, the signal received by the coil on that side will increase. The plasma density is a function of the position, and therefore also the average phase difference between the two legs of the interfero!Teter.
KLYSTRON
WAVE GUIDE
ATTENUATOR
Thus, the electron density is a linear function of the phase shift or the number of output fringes when the micro1t1ave frequency satisfies the above condition, (r};w~e(x)) » 1. The mi crmvave interferometer frequency used in the tokamak i Cal technology is 60 GHz. The source of uncertainty comes from noise superimposed on the interference signal from the detector.
The conditions at the edge of the plasma are sufficiently mild that Langmuir probes can be used to measure the local electron density and. Four of the channels have a frequency of one microsecond per word, so the maximum frequency response using the four-word resolution is about 200 kHz. The remaining channels have a frequency of 5 microseconds per word, so the frequency response at a resolution of four words is about 40 kHz.
The transient recorder can also drive an analog pen plotter so that hard copies of the signal can be produced. The first step in studying magnetosonic cavity modes is to observe them through a receiving probe placed 180° to the day from a transmitting antenna (Figure 4. 1). Finally, the antenna must be kept away from the central plasma region where most of the damage to the antenna will occur.
A stainless steel tube provides a mechanical feed from the outside into the vacuum chamber. The antenna can be moved radially into and out of the plasma through the vacuum ring seal.
300WATT AMP
CURRENT PROBE
PHASE DETECTOR
A matching network consists of a variable series capacitor used to tune the inductance of the antenna and an R.F. However, as mentioned in Section 4.1, the antenna loop area is determined by the size of the port in the tokamak and the maximum distance that the antenna can protrude into the plasma without suffering damage to the antenna. The resistance of the antenna is reduced by using material with better conductivity and by increasing the size of the conductor.
The conductor used in the antenna is changed from 16 gauge tungsten wire to l/8 inch diameter copper tubing. The measured Q of the bare copper antenna is about 130 at 10 MHz, and the inductance of the antenna is about .46 microhenry. Second, the winding ratio on the transformer is fixed, so the generator impedance can only match at one frequency, from the antenna.
Details on antenna dimensions and capacitor values in the matching network are covered in Appendix a. The efficiency, n, depends on the plasma load resistance and the antenna resistance, Rant' in the following v1ay [equation (2. 7.1)]. One way to obtain the loading resistance of the plasma is to reduce the incident power, the reflected power at the antenna and the antenna current.
As indicated in equations (2.6.1) and (2.6.2), the incident and reflected pm·Jer in the antenna can be derived from the incident and reflected voltages measured with a VHF directional coupler placed between the generator and the antenna matching network is. . To obtain the complex load impedance of the plasma at a cavity resonance, the phase difference between the incident and the reflected voltage in the antenna must be measured.
MIXER (SN7514)
SIGNAL INPUT (f)
FILTER
THRESHOLD -=
ZERO CROSSING COMPARATOR
THRESHOLD DETECTOR
CLEAR
74LSOO 74LS04
200 KHz 1 PHA LO\V PASS SE
THRESHOLD 1-j THRESHOLD I
ADJ. = DETECTOR I MHz
FILTER I OUTPUT
74LSOO
EXPERIMENTAL RESULTS 5.1 Transmission Measurements
One of the observations in the experiment is that no cavity mode was observed at frequencies below 7 MHz. The input frequency is normalized to the ion cyclotron at the center of the tokamak, i.e. 6 MHz. Various properties of the amplitude and phase detectors, and the experimental conditions, can help in understanding some of the.
First, the antenna was matched to the impedance of the generator in the absence of plasma. At this point, c1 and c2 were adjusted again to reduce the reflected voltage in the presence of plasma. First, the impedance of the antenna was obtained in a vacuum chamber by measuring the values of the tuning capacitors c1 and c2 (see columns 3 and 4).
When the antenna is completely outside the tokamak chamber and in port, for example, the plasma charge is zero. Experimental results of the plasma loading resistance, R, in the different cavity modes are presented in this section. The presentation of experimental data on plasma loading resistance at cavity resonances is divided into two parts.
Second, the magnitude of the plasma load resistance for the different cavity states at different input frequencies is summarized in Tables 5.1 and 5.2. As stated in the introduction, the main emphasis in this thesis is on measuring the complex plasma load impedance in the cavity states.
2rrt
TO GLAS
The resistance and inductance of the antenna are a function of the distance from which the antenna protrudes into the vacuum chamber of the tokamak. The reason for this dependence on distance into the vacuum chamber is in the 6 x 4 x l inch stainless steel opening where the antenna sits when it is completely outside the tokamak vacuum chamber. The effect of the stainless steel connector is to lower the antenna inductance and increase the antenna resistance due to eddy current losses in the connector wall.
Therefore, as the antenna moves out of the port and into the vacuum chamber, the antenna inductance should show an increase with distance and the antenna resistance should show a decrease with distance. The data on the resistance of the antenna as a function of the distance in the tokamak chamber are shown in figure a.2. The inductance of the antenna measured in the experiment is approximately independent of the input frequency, and the resistance of the antenna increases with an increase in the input frequency.
Frequency f (MHz)
The axial magnetic field makes the plasma anistropic; Thus, the dielectric property of the plasma must be expressed as a tensor quantity. Determine a time-dependent overall displacement, D, ejwt for the plasma [16]. is the current density of zn is the ionic charge, q. n is the sign of the dielectric tensor. The periodic boundary condition is imposed in the z-direction to simulate the closure of the torus.
Since there are two branches of the dispersion relation (b.l7), one can control the polarization of waves propagating along the longitudinal d.c. When these solutions are substituted into equation (b.20) and the dielectric tensor definition (b.3) is used, the following polarizations are found for both branches. Since the tokamak has a conducting wall, consider the solution of the magnetosonic wave in a cylindrical cavity.
To simulate the closure of the tokamak on itself, periodic boundary condition is imposed in the axial direction (i.e. k = N/R where R = main radius of the tokamak, see Fig. b. 1). It is important to estimate the resistive load of the wave due to the finite conductivity of the tokamak \vall, and to compare the calculated value with the measured resistive load in the low-power experiment. One approach to estimating Qw is to calculate the attenuation reduction, y, of the cavity modes due to the finite resistivity of the cavity wall.
The attenuation decrement is defined as the attenuation of the electromagnetic radiation in the cavity per time unit. The real part of the expression on the right is the wall resistance, and the imaginary part is the additional reactance from 111all.
