King J D, Makowski M A, Holcomb C T, Allen S L, Geer R, Meyer W H, Hill D N, Pham D, Morse E C
Lawrence Livermore National Laboratory, Livermore, California 94550, USA.
Rev Sci Instrum. 2010 Oct;81(10):10D739. doi: 10.1063/1.3496989.
The use of lock-in amplifiers for phase sensitive detection of motional Stark effect (MSE) diagnostic signals is of critical importance to real-time internal current profile measurements in tokamak plasmas. A digital lock-in (DLI) upgrade utilizing field programable gate array firmware has been installed on the MSE system of the DIII-D tokamak for the eventual replacement of largely obsolete analog units. While the new digital system has shown a small reduction in electronic noise over the analog, the main advantages are reduced cost, hardware simplicity, compact size, and phase tracking during plasma operations. DLI recovery of MSE polarization angles was accomplished through use of reference processing to produce only photoelastic modulator (PEM) second harmonic frequencies and electronic signal processing to maximize the fidelity of the recovered signal. A simplified discrete analytical solution was found that accurately describes the new DLI hardware. The DLI algorithm was found to cause a prohibitively large oscillating artifact atop the demodulated signal. The artifact was caused by the accumulator interval not containing an exact integer number of PEM multiplier periods. Successful MSE measurements require the minimization of this oscillating artifact amplitude. The analytical solution was used to select an appropriate accumulator interval that both reduces the artifact and maintains the greatest temporal resolution possible. Sample EFIT equilibria reconstructions and corresponding safety factor profiles showed very close agreement between the analog and digital lock-ins.
