The &agnostic study allowed investigation of the spatial shape of the RF current driven by the electric field antennas in the peripheral plasma. First, the resonant build-up of the electric field at the antenna causes an increase in the load resistance of the antenna.
Wave Theory
Review of Cold Plasma Wave Theory
- Cold Plasma Dielectric Tensor
- Plane Waves
- Phase and Group Velocity Surfaces
The dispersion relation can be rearranged to yield 8 as a function of the plasma parameters and of n. Polar plots of the ratio of the vacuum electric field energy to the magnetic field energy (a), and the ratio of the particle kinetic energy to the magnetic field energy (b), for a plane wave, as a function of the angle of propagation (8 ) with respect to the static magnetic field.
Toroidal Eigenmodes .1 Introduction
- Relations Between Field Components
- Boundary Conditions
- Zero Electron Mass Approximation
The radius of the cylinder ( p o ) is equal to the minor radius of the torus, while the length of the cylinder ( L ) is equal to the major circumference of the torus (2nR). The tangential components of the electric field (E, and E B) and the normal component of the magnetic field (3,) must vanish so a t p = p.
Wave Damping
- Introduction
- Cyclotron Damping
- Landau Damping and TTMP
- Resistive Wall Damping
- Insulating Gap Damping
- Collisional Damping
- Comparison
Plots of the Qs of the N = 1-5, m = 1, L = 1 toroidal eigenmodes, as functions of the ion temperature, for fundamental cyclotron damping. Here w/2n = 8 MHz, B0 = 5.26 kG, and the ion cyclotron resonance layer passes through the center of the plasma. Here o/ 2n = 12 MHz, B0 = 3.95 kG, and the second-harmonic resonance layer passes through the center of the plasma; the fundamental resonance layer is not in the tokamak.
Radial Density Profile
- Numerical Model
- Effects on Eigenmode Dispersion Curves
- Effects on Field Profiles
The transverse gradient of the field is seen to be extremely sensitive to the ramal density perturbations: for the a = 0. A complete calculation of the Q's expected for the eigenmodes using these density perturbations has yet to be performed. The horizontal axis in each plot is the radius p; the limits of the axis a r e 0 (left side) and po (right side).
Other Effects
- Poloidal Magnetic Field
- Toroidd Geometry
For parameters typical of the Caltech tokamak, the relative shift in density of the resonances associated with a plus and minus N toroidal mode number pair is small (typically <5%). Resonances due to a wave traveling in one direction (i.e., plus or minus N mode only) are traveling wave resonances and the magnitude of the wave fields should not vary as a function of toroidal angle. However, if the resonances due to the k N modes overlap substantially (the resonances have a finite width due to damping), then the modes become standing wave resonances and the amplitude of the fields must have nodes and peaks as a function of the torus angle. .
Vacuum Vessel
The largest, whose cross-section measured 9.8 cm high x 4.7 cm wide, was connected via a 14 cm internal diameter to a high-vacuum pump. A port with an internal diameter of 10 cm was later welded into the elbow to allow the use of a pumping port for the RF antennas. There were five doors measuring 9.8 cm high x 2.2 cm wide; they were located, like the pumping port, on the median plane around the outer radius of the chamber (R = Ro + a).
Coil Design
This set of coils was powered independently of the toroidal field by a separate DC supply. The error correction of the toroidal field had a major effect on the tokamak's performance. Several ohmic heating field flux lines are shown, including the small coil radius.
Power Supplies
The two halves of the slow bank can be connected in series or parallel to provide further flexibility. The slow bank, consisting of 400 fiF of capacitance, was charged to 40 -60 V and fed into the coil when the voltage on the fast bank had decayed to the level of the voltage on the slow bank. To ensure a reliable initial plasma breakdown, a 1.5 mF capacitor, charged to 6 - 9 kV, was discharged into the ohmic heater coil about 2 msec prior to switching on the main ohmic heater bank.
The time variation of the above signals was quite slow, so anti-aliasing filters were generally not necessary. A plug-in module for the CAMAC-krat2 allowed automatic display of the sixteen data channels on CRT monitors after the tokamak recording and also allowed the transfer of the data to the computer. Twelve of the buffers had a -3 dB bandwidth of 250 kHz; the other four had a bandwidth of 1 MHz.
Diagnostics
A microwave interferometer operating at t 75 GHz measured the average electron density along a vertical chord through the center of the tokamak. The additional phase shift of the microwave signal passing through the tokamak chamber due to the presence of the plasma is approx. The photoelectric current from the panel was measured and was proportional to the incident UV photon flux; detector response was approximately from 20 to 120 nm ("soft" UV range).
Discharge Cleaning
The detector consisted simply of a bare slab of tungsten placed in one of the lower ports of the tokamak and suitably shielded from the plasma. Although the dynamics of the chemical processes occurring in the plasma have not been well defined, the overall effect on tokamak performance is dramatic. The evolution of impurity levels in the neutral gas of the tokamak during discharge cleaning was monitored with a quadrupole residual gas analyzer (Varian VGA-100); the relative impurity levels required for clean tokamak operation have been established through experience.
Gas puffing also shortened the plasma's overall lifespan. Without gas puffing, recording lengths of 20 msec were easily obtained; with gas p u f i g to a density of about 1 0 I 3 the maximum shot lengths were 10 - 15 msec.
Plasma Characteristics
The soft UV signal is the most useful indicator of the degree of impurity in the machine. Typically, about 10% of the shocks simply failed to form a plasma during start-up because one of the ignitrons did not fire properly. About 15% of the remaining recordings were usually unsatisfactory because their density or current development was abnormal.
Charge-Exchange Diagnostic
- Introduction
- Design and Construction
- Operation
Most of the neutral charge exchange flux received by the &agnostic originates from the low-temperature region near the plasma edge. A photograph of the tokamak laboratory showing the installed charge exchange spectrometer is shown in Figure 3-1 1. No problems were observed with contamination of the tokamak from nitrogen from the stripping cell.
ENERGY (EV)
CHAPTER 4
Apparatus
RF System Design
- RF Exciters
- System Grounding
The power supplies for equipment to be connected to the vacuum chamber (ie, the tokamak turbo pump, the data acquisition system console, and the RF source cabinet) were isolated from the building ground using electrostatically shielded isolation transformers. The chassis ground of the data acquisition console was connected to the tokamak system ground using a 3.8 cm diameter copper pipe attached to the RF impedance matching box. The RF source cabinet ground was only connected to the tokamak system ground through the jacket of the RF output transmission line, which was also connected to the impedance matching box.
TOKAMAK LAB
ADJOINING LAB
RF EXCITER HIGH POWER AND
CABINET
High Power Amplifier .1 Introduction
- RF Design
- Construction
- Operation
An impedance increase was necessary to match the impedance of the driver amplifier (50 R) to that of the grid circuit (1500 R). The output tank circuit consisted of a C-L-C n network that transformed the tube's resonant plate impedance (4 - 600 R for typical operating conditions3) to the desired output impedance (RL = 50 R). The water jacket covering the tube anode was at a DC potential of 15 - 20 kV during amplifier operation.
Directional Coupler
The basic idea is that the voltage across the loop results from contributions from capacitive coupling to the center element of the coaxial line and from magnetic coupling to the current carried by the center element. The coaxial section for the coupler was only a 10 cm length of RG-17 cable. The loop was formed by simply inserting an insulated wire between the outer conductor (copper braid) and the dielectric insulation of the cable.
REFLECTED OUTPUT
Impedance Patching Network
- Introduction
- Design
For efficient transfer of RF energy into the plasma, it is necessary to match the impedance of the generator (50 R) with that represented by the antenna in the plasma. The reactive part of the antenna impedance usually decreases slightly as the plasma density increases (for all antennas), but rarely by more than -10%. The impedance seen by the matching network, however, was the impedance ZLo of the antenna as transformed by the antenna feed tube.
ANTENNA
- Construction
- Linear RF' Detectors
- RF Phase Detectors .1 Introduction
- DBM Phase Detector
- sin(~t t +) 0 t i 2 DBM2 IF FILTER AND oV2a ApsinO
The characteristics of the RF signals from the antenna voltage and current monitors were slightly different. When two signals of the same frequency are applied to the RF and LO (local oscillator) ports of a DBM, the DC component of the output at the IF (intermediate frequency) port is a function of the phase difference between the signals. The dynamic range of the system (important for magnetic probe measurements) is limited due to the proportionality of the output voltage to the amplitude of the input signal (the data recording system has a fixed dynamic range of 48 dB).
LOW PASS
AMPLIFIER
- Digital Phase Detector
The relative phase between two RF sinusoids is proportional to the time interval T ~ , between successive positive (or negative)-going zero crossings of the signals: p = ~ T T , , / T ~ , where ~ d is the RF period. The output of this device will then consist of a series of pulses whose duty cycle will be proportional to the input phase difference. As long as the positive-going transition to the Ck: input occurs while R is low, the output at Q is a pulse-width modulated square wave whose duty cycle is linearly proportional to the phase difference between the inputs a t Ck and R.
PHASE OUTPUT
Harmonic Distortion
If a harmonic of the fundamental frequency is added to the input, the transition times are shifted. Vh = A o sin(oot) +An sin(n wet + p,) , the positive crossing through zero that occurred t t = 0 before the introduction of the harmonic now occurs at about the same time. Thus, the amplitude of the harmonic must be at least 55 db below the fundamental amplitude of the harmonic to keep the error caused by the harmonic less than 0.1 degrees (which is required in some impedance measurement experiments).
Dynamic Range
The change in detector output as the input amplitude decreases is mainly due to the offset input voltage and the final gain of the comparators. Improvements in dynamic range can be achieved by increasing the input stage gain and by reducing the input offset voltage. In addition, the magnitudes of the current and voltage signals for the impedance measurements changed closely synchronously during the plasma shot (because / Zmt 1 did not change much), which tended to reduce the phase errors.
CHAPTER 5
RF Antennas and Plasrna Probes
RF Antennas
- Antenna Feedthru Assembly
- Bare Loop Antenna
- Ceramic-Insulated b o p Antenna
- Faraday-Shielded Loop Antenna
- Bare Plate Antenna
The Q of the antenna (the ratio of its reactance to its resistance), including the antenna feed tube, was measured using the method described by DeMaw [1976]. Several small probes were made that could be attached to the side of the Macor box (the magnetic and Langmuir probes are shown in Figure 5-7). The first such structure investigated consisted of a bare copper rectangle (5.1 mm long x 3.8 cm wide x 1.5 mm thick) connected to the inner element of the antenna feed tube (Figure 5-9).
Vacuum Fields
