Method and apparatus for recirculation with control of synchrotron radiation
A method for controlling beam quality degradation from ISR and CSR and stabilizing the microbunching instability (μBI) in a high brightness electron beam. The method includes providing a super-periodic second order achromat line with each super period being individually linearly achromatic and isochronous, setting individual superperiod tunes to rational fractions of an integer (such as 4 th or 6 th integers), setting individual bend angles to be as small as practical to reduce driving terms due to dispersion and dispersive angle, and setting bend radii as large enough to suppress ISR but not negatively affect the radial dependence of CSR. The method includes setting the structure of the individual superperiods to minimize bend plane beam envelope values in the dipoles to reduce betatron response to a CSR event at a dispersed location, increasing beam angular divergence, and creating dispersion nodes in the dipoles to similarly reduce response to CSR events, and limit R 56 modulation in order to mitigate μBI.
1. A method of controlling incoherent synchrotron radiation (ISR) and coherent synchrotron radiation (CSR) in a high brightness electron beam comprising:
a. providing a super-periodic second order achromat line comprising a plurality of superperiods, wherein each superperiod in said plurality of superperiods includes a plurality of dipoles and quadrupoles and each superperiod is linearly achromatic and isochronous, the electron beam including a bend angle and a bend radius at each of said dipoles;
b. providing a tune for each superperiod, wherein each of the tunes provides the frequency of the transverse oscillation for the corresponding superperiod;
c. setting the tune for each superperiod to a rational fraction of an integer;
d. setting small individual bend angles to reduce driving terms due to dispersion and dispersive angle; and
e. setting the bend radius of the electron beam at each of said dipoles to a value that will suppress ISR and will limit the radial dependence of CSR.
2. The method of claim 1 , wherein said dipoles and quadrupoles are arranged in a superperiod structure and each of said dipoles includes a bend plane beam envelope value, said electron beam includes a betatron response, a beam angular divergence, a dispersion pattern, an angular error associated with a CSR event at a location of nonzero dispersive angle, and a microbunching instability derived from modulation in the longitudinal phase space distribution, wherein the method further comprises
a) minimizing the bend plane beam envelope values in the dipoles to reduce betatron response to a CSR event at a dispersed location;
b) increasing the beam angular divergence, thus reducing the size of the angular error associated with a CSR event at a location of nonzero dispersive angle;
c) providing dispersion nodes in the dipoles to reduce response to CSR events; and
d) limiting momentum compaction (R 56 ) modulation in order to reduce the microbunching instability (μBI).