Microwave Resonance Shift Method in Stellarator Plasma Density Measurements

To investigate the trapping efficiency of a hot electron plasma and its confinement in a toroidal magnetic field configuration, a small, adiabatically heated, symmetric stellarator has been constructed. Various diagnostics methods are used to find various plasma parameters: electron density and temperature, confinement time, etc. One technique to find electron density and confinement time is to use the microwave cavity frequency shift method. This method is especially applicable in the case of this stellarator since the size of the stainless steel toroidal container is such that it can support the lowest resonant modes with frequencies about 4GHz. The resonance frequency shift method pertaining to a cylindrical resonator is reviewed and the theory applicable to the toroidal geometry is discussed. The resonant mode structure in a toroidal resonator will be described. It is shown in numerical examples that the presence of plasma will cause a considerable shift in the resonant frequency of the cavity. This frequency shift is directly proportional to plasma density and is also influenced by the magnetic field. The system has been built and is described in some detail. A fundamental transistor oscillator, which can be swept over a 0 to 300MHz bandwidth in the range of 2 to 4GHz, provides the microwave signal. An oscilloscope provides a sweep voltage which is conditioned to control the oscillator frequency. A staircase voltage is generated which is used along with the horizontal sweep to form a raster of 1 to 64 lines on the oscilloscope.