The vector potential and stored energy of thin cosine (n{theta}) helical wiggler magnet

Technical Report · Fri Dec 01 04:00:00 EST 1995

DOI:https://doi.org/10.2172/207361· OSTI ID:207361

Caspi, S

Expressions for pure multipole field components that are present in helical devices have been derived from a current distribution on the surface of an infinitely thin cylinder of radius R. The strength of such magnetic fields varies purely as a Fourier sinusoidal series of the longitudinal coordinate Z in proportion to cos(n{theta}- {omega}{sub m}z), where {omega}{sub m} = (2m-1){pi}/L, L denotes the half-period and m = 1, 2, 3 etc. As an alternative to describing such field components as given by the negative gradient of a scalar potential function (Appendix A), one of course can derive these same fields as the curle of a vector potential function {rvec A}--specifically one for which {nabla} {times} {nabla} {times} {rvec A} = 0 and {nabla}{center_dot}{rvec A} = 0. It is noted that we seek a divergence-free vector that exhibits continuity in any of its components across the interface r = R, a feature that is free of possible concern when applying Stokes` theorem in connection with this form of vector potential. Alternative simpler forms of vector potential, that individually are divergence-free in their respective regions (r < R and r > R), do not exhibit full continuity on r = R and whose curl evaluations provide in these respective regions the correct components of magnetic field are not considered here. Such alternative forms must differ merely by the gradient of scalar functions that with the divergence-free property are required to be ``harmonic`` ({nabla}{sup 2}{Psi} = 0).

• Research Organization: Lawrence Berkeley Lab., CA (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 207361
• Report Number(s): LBL--38075; ON: DE96005012
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
66 PHYSICS
99 GENERAL AND MISCELLANEOUS
INTEGRAL EQUATIONS
MAGNETIC FIELDS
MATHEMATICAL MODELS
POTENTIALS
POWER SERIES
WIGGLER MAGNETS