20
An Introduction to Beam Physics
FIGURE 1.15: Sketch of the first Free Electron Laser (FEL). (Reprinted
with permission from J. M. J. Madey, J. Appl. Phys., 42:1906, 1971 [47].
Copyright 1971, AIP Publishing LLC.)
m = γ · m 0 . Commonly the ratio of momentum and charge p/q is denoted by
χ m and called magnetic rigidity; we apparently have
χ m =
p
q
= Bρ.
Because χ m = Bρ, the magnetic rigidity has the unit Tesla meter (Tm), and
is frequently simply referred to as B rho.
In the case of the betatron, both bending and acceleration come from the
same source, namely a magnetic field the strength of which increases with
time in such a way that its magnitude matches the increasing energy of the
particles to keep them at nearly constant radius, and the circular induced
electric field provides the acceleration for the particles. Fig. 1.16 shows a
sketch of the betatron [37, 38].
It is worthwhile to note that the basic idea of utilizing an electric field
produced by a changing magnetic field also occurs in an application from
daily life: certain modern cooking surfaces. In this case, the electrons that
are accelerated are not within the vacuum of a beam pipe, but merely in the
metal that constitutes the bottom of the pot used for cooking; and of course
since their mean free path is short, they do not attain high energies before
colliding with either other electrons or the lattice atoms, thus transferring
their whole kinetic energy to heat.
A quantitative understanding begins with Faraday’s law of induction, now
one of Maxwell’s equations:
∇ ×
E = −
∂
B
∂t
,
An Introduction to Beam Physics
FIGURE 1.15: Sketch of the first Free Electron Laser (FEL). (Reprinted
with permission from J. M. J. Madey, J. Appl. Phys., 42:1906, 1971 [47].
Copyright 1971, AIP Publishing LLC.)
m = γ · m 0 . Commonly the ratio of momentum and charge p/q is denoted by
χ m and called magnetic rigidity; we apparently have
χ m =
p
q
= Bρ.
Because χ m = Bρ, the magnetic rigidity has the unit Tesla meter (Tm), and
is frequently simply referred to as B rho.
In the case of the betatron, both bending and acceleration come from the
same source, namely a magnetic field the strength of which increases with
time in such a way that its magnitude matches the increasing energy of the
particles to keep them at nearly constant radius, and the circular induced
electric field provides the acceleration for the particles. Fig. 1.16 shows a
sketch of the betatron [37, 38].
It is worthwhile to note that the basic idea of utilizing an electric field
produced by a changing magnetic field also occurs in an application from
daily life: certain modern cooking surfaces. In this case, the electrons that
are accelerated are not within the vacuum of a beam pipe, but merely in the
metal that constitutes the bottom of the pot used for cooking; and of course
since their mean free path is short, they do not attain high energies before
colliding with either other electrons or the lattice atoms, thus transferring
their whole kinetic energy to heat.
A quantitative understanding begins with Faraday’s law of induction, now
one of Maxwell’s equations:
∇ ×
E = −
∂
B
∂t
,