US 12,295,091 B2
Method for obtaining strong focusing of isochronous accelerator by varying magnetic field gradient in large radial range
Tianjue Zhang, Beijing (CN); Wei Fu, Beijing (CN); and Chuan Wang, Beijing (CN)
Assigned to CHINA INSTITUTE OF ATOMIC ENERGY, Beijing (CN)
Filed by CHINA INSTITUTE OF ATOMIC ENERGY, Beijing (CN)
Filed on Jun. 27, 2023, as Appl. No. 18/214,566.
Application 18/214,566 is a continuation of application No. PCT/CN2022/119570, filed on Sep. 19, 2022.
Claims priority of application No. 202210748317.8 (CN), filed on Jun. 29, 2022.
Prior Publication US 2024/0008166 A1, Jan. 4, 2024
Int. Cl. H05H 13/00 (2006.01)
CPC H05H 13/005 (2013.01) 7 Claims
OG exemplary drawing
 
1. A method for obtaining strong focusing of an isochronous accelerator by varying a magnetic field gradient in a large radial range, wherein a main magnet of the isochronous accelerator provides a bending effect and a focusing effect, which is equivalent to effects of using of quadrupole, sextupole, and octupole magnets in a synchrotron accelerator; the method comprises: introducing a first-order, a second-order, and a third-order magnetic field gradients in the large radial range of the main magnet of the isochronous accelerator to achieve an enhanced focusing, compensation of chromaticity, handling of resonances similar to that provided by a quadrupole, a sextupole, and octupole lenses, and obtain a transverse focusing force required for an isochronous continuous wave acceleration from 1 GeV to 2 GeV;
wherein providing, by the main magnet of isochronous accelerators, the bending effect and the focusing effect comprises:
1) Using a magnetic field with an angularly varying gradient as a main source of an axial focusing force, wherein, a magnetic field distribution is given by a formula of:
B(r,θ)=B0γ(r)[1+f cos Nθ],N≥3  (1)
wherein B0 is a central magnetic field, γ is a relativistic factor, N is a number of sectors, f is a flutter of a magnetic field and θ is an angular position; and
2) varying the magnetic field gradient radially to simultaneously vary a peak region magnetic field B(r) in a radial direction to satisfy a polynomial form:

OG Complex Work Unit Math
wherein ai is a magnetic field gradient adjustment coefficient, r is a closed orbit radius, i is an order of the magnetic field gradient ranging from 0 to n, wherein, the focusing effect refers to a change in an orbit radius of a particle when the particle passes through a magnetic peak region during a cyclotron motion, in addition to a deflection effect caused by the varying magnetic field gradient in different regions
wherein introducing the first-order magnetic field gradient in the large radial range of the main magnet of the isochronous accelerator to achieve the enhanced focusing similar to that provided by the quadrupole lens comprises:
(1) solving for a radial oscillation frequency vx and an axial oscillation frequency vz of the first-order magnetic field gradient; and
(2) solving for the magnetic field gradient adjustment coefficient ai in the formula (2) by solving a system of equations, where i ranges from 0 to 1.