Abstract: As a fundamental plasma oscillation the compressional Alfven waves (CAW) are interesting for plasma scientists both academically and in applications for fusion plasmas. They are believed to be responsible for the ion cyclotron emission (ICE) observed in many tokamaks. The theory of CAW and ICE was significantly advanced at the end of 20th century in particular motivated by first DT experiments on TFTR and subsequent JET DT experimental studies. More recently, ICE theory was advanced by ST (or spherical torus) experiments with the detailed theoretical and experimental studies of the properties of each instability signal. There the instability responsible for ICE signals previously indistinguishable in high aspect ratio tokamaks became the subjects of experimental studies. We discuss further the prospects of ICE theory and its applications for future burning plasma (BP) experiments such as the ITER tokamak-reactor prototype being build in France where neutrons and gamma rays escaping the plasma create extremely challenging conditions for fusion alpha particle diagnostics.

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