Space Charge Compensation (SSC) in hadron beams
Longitudinal space-charge fields can generate substantial distortion of the rf-generated potential wells, fill the extraction kicker gap in the beam, affect the incoherent synchrotron tune spread, and have the potential for causing instability and longitudinal emittance growth. The net effective voltage per turn resulting from the space-charge self voltage and the ring inductive wall impedance ?0L is proportional to the slope of the beam current distribution e{beta}c {lambda}(s) and can be expressed as: V{sub s} = {partial_derivative}{lambda}(s)/{partial_derivative}s [g{sub 0}Z{sub 0}/2{beta}{gamma}{sup 2} - {omega}{sub 0}L]e{beta}cR where R = c/{omega}{sub 0} is the average machine radius, Z{sub 0} = 377 Ohm and g{sub 0} = 1 + 2ln(b/a) is the geometric space-charge constant, a and b are the beam radii and vacuum-chamber aperture. By introduction a tunable inductance L, e.g. of ferrite rings, the term in brackets and, consequently, the space-charge effect may be substantially reduced or canceled at some chosen energy [1]. This concept has been experimentally proven at the LANL Proton Storage Ring at LANL where three inductive inserts, each consisting of 30 'cores' of a cylindrically shaped ferrite with thickness of 1 inch, inner diameter of 5 inches, and an outer diameter of 8 inches, were installed. The magnetic permeability of the ferrite could be adjusted by introducing current into solenoids wound around the ferrite so that in the MHz range of frequencies the longitudinal space charge impedance of the machine was compensated. A strong longitudinal instability was noticed at much higher frequencies of about 75 MHz, but it was later suppressed by heating the ferrite to a temperature of 130 C to make it more lossy.
- Research Organization:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- AC02-07CH11359
- OSTI ID:
- 1038149
- Report Number(s):
- FERMILAB-PUB-10-097-APC; TRN: US1201800
- Country of Publication:
- United States
- Language:
- English
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