1995
DOI: 10.1103/physreve.51.4947
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Effects of a nonlinear damping force in synchrotrons with electron cooling

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Cited by 9 publications
(4 citation statements)
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“…For such low effective velocity, the single-particle friction force would have a maximum around this small value having a non-linear decrease of the force for larger velocities. As a result, significant large-amplitude oscillations for the relative velocities corresponding to the non-linear part of the force are expected [7]. However, we did not see such oscillations for the velocities in this range.…”
Section: Fitting Experimental Curvesmentioning
confidence: 59%
See 1 more Smart Citation
“…For such low effective velocity, the single-particle friction force would have a maximum around this small value having a non-linear decrease of the force for larger velocities. As a result, significant large-amplitude oscillations for the relative velocities corresponding to the non-linear part of the force are expected [7]. However, we did not see such oscillations for the velocities in this range.…”
Section: Fitting Experimental Curvesmentioning
confidence: 59%
“…In our experiments, changing the FW frequency by a few Hz resulted in a very fine step in relative velocity. A similar technique was used ,successfully before, for example at IUCF [7]. In experiments reported in this paper, the longitudinal friction force curves were measured for protons at the injection energy of 48 MeV.…”
Section: Measurement Approachmentioning
confidence: 99%
“…Mathematically, this corresponds to a Hopf bifurcation. This phenomenon was observed and investigated in the Cooler (33)(34)(35), and it was demonstrated that one could make use of it to measure the temperature of the electron beam.…”
Section: Electron Coolingmentioning
confidence: 98%
“…The phase.shift.method has been employed earlier in different varieties at CELSIUS [5] and at other laboratories such as IUCF [6], TSR [7] and MSL [8]. ' …”
Section: Methodsmentioning
confidence: 99%