Analysis of the longitudinal microwave instability for heavy ion fusion

Tariq Majeed, Purdue University

Abstract

A theoretical model has been developed to analyze the experimental observations of the longitudinal microwave instabilities in reference to the joint experiment between the Argonne National Laboratory and the Rutherford Appleton Laboratory in the UK. The longitudinal microwave instability (LMI) of a coasting beam is created by the interaction of the electromagnetic fields of the ion beam and the surrounding cavity structures in an accelerator storage ring. The Keil-Schnell stability criteria have been used in the present analysis in predicting the LMI threshold limits and the LMI saturation points in the ISIS storage rings for 70-MeV coasting proton beams. The higher and lower values of the LMI threshold limits have been attributed to the magnitudes of the initial $\Delta$p/p of the beam. The LMI saturation point is almost unaffected by the initial conditions of the beam, and the theoretically calculated values are 3.795 $\times$ 10$\sp{12}$ for debuncher-off case and 3.935 $\times$ 10$\sp{12}$ for debuncher-on case. With the sweeper magnet-on, the calculated values of the saturation points are 3.924 $\times$ 10$\sp{12}$ and 3.883 $\times$ 10$\sp{12}$ for debuncher-off and debuncher-on, respectively. The differences of the number of particles related with the initial threshold limits and the saturation point (though very close) are believed to be the reason of the difference in the signal height from the spectrum analyzer. The calculated values of LMI rise time are within 5% to 12% of the experimentally observed values. With the sweeper magnet-on, a delay in the start of LMI and the faster growth rates of $\Delta$p/p in the later stages of injection have been observed experimentally and are predicted by the developed analytical model. The difference of the LMI signal height between the debuncher on and off cases, while the sweeper magnet is on, is about 20%. It has also been observed in the experiment that the application of external RF voltage of 120 volts/turn was able to reduce the signal height significantly and 140 volts/turn was sufficient to suppress the signal completely. Both of these phenomena are predicted by the present theoretical analysis. However, the value of the RF voltage (V$\sb{\rm RF}$) which is sufficient to suppress the LMI is calculated to be close to 160 volts/turn. A higher value of RF voltage is predicted for the beam of lower initial $\Delta$p/p. The effect of V$\sb{\rm RF}$ indicates that it is the overall $\Delta$p/p of the beam that grows and causes the saturation of LMI above the threshold limits, not just a tail in the momentum distribution of the beam containing a few percent of the beam particles. The application of the small values of V$\sb{\rm RF}$, e.g., in the range of 160 to 350 volts/turn, would provide a good suppression mechanism for LMI problem.

Degree

Ph.D.

Advisors

Choi, Purdue University.

Subject Area

Nuclear physics|Particle physics|Atoms & subatomic particles

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