Radio frequency heating coils for shock wave experiments

Radio-frequency eddy current heating of metallic samples in shock wave, ultrasonic and diamond anvil apparatus provides a methodology for obtaining hot samples or hot metallic gaskets (containing a sample) and yet not heating the entire target, ultrasonic assembly or diamond cell. Analysis of a previous design of a radio-frequency (∼0.5 MHz) coil demonstrated that the center of 13 mm diameter shock wave experiment sample discs were underheated and the experimental temperatures achieved resulted from conduction of heat from the overheated sample edges relative to the center of the sample. We show, using the Biot-Savant law, that the ratio of magnetic field in the center to that at the edge of the sample, f, can be maximized to a value of f=1.8, by decreasing the radius of the heater coil, relative to the 13 mm diameter of sample. A simple analysis provides the thermal gradient across the sample thickness. An electric skin depth for iron of ∼1 mm for the 0.45 MHz frequency of the heater power supply of our system is obtained. This leads to a maximum temperature gradient of ∼52 K over the 4 mm thickness of the shock wave sample discs.