Beams and Beam Physics
19
through modulation of the vanes. Similar to the drift tubes, the particles are
accelerated throughout the structure when the distance between the peak and
the neighboring valley satisfies
L i =
1
2
v i T rf .
In general, linacs can provide beams of high current, and of higher energies than static accelerators, yet because of the single use of each electric
field, they are still rather expensive per MeV. Linacs are frequently used as
pre-accelerators for accelerators of higher energies. They also have the distinctive advantage that they avoid synchrotron radiation, which is often
a limiting factor in circular accelerators for light particles. This aspect is
very important for electron and positron high energy accelerators such as the
Stanford Linear Collider (SLC) at SLAC National Accelerator Laboratory,
California, USA. It is the main reason for the interest in next generation
Linear Colliders, such as plans being considered for an International Linear
Collider (ILC), where a pair of two linacs shoot electrons and positrons at
each other at very high energy.
Recently, linear accelerators have been widely used in producing a free
electron laser (FEL), whose high peak brightness and short pulse duration
has opened up unprecedented opportunities for scientific investigations. Fig.
1.15 shows the setup of the first FEL experiment. Electrons go through a
magnetic device called the undulator, which consists of alternating magnetic
poles. As a result, the trajectory of such an electron is very similar to a sine
function, causing the emitted photon field to add coherently. Together with
the large number of periods, the peak intensity of the X-ray can be orders
of magnitude higher than that from a circular accelerator (see the following
subsection). The advantage of a linac is that it can produce an electron beam
with smaller emittance and shorter pulse duration.
1.3.3 Circular Accelerators
Arguably the simplest circular accelerator is the betatron, which, besides
its practical use as a compact accelerator for lower energies, also represents
an excellent textbook style application of principles of electrodynamics. In
the case of the betatron, the orbit follows a circular shape, which is achieved
by a magnetic field. If the motion is perpendicular to the magnetic field, then
we have in SI units
mv
2
ρ
= qvB, and so ρ =
mv
qB
=
p
qB
,
and so the radius of motion depends only on the momentum and charge of
the particle as well as the magnetic field. Note that the equation is correct
even in the relativistic case, if m is understood to mean the relativistic mass
19
through modulation of the vanes. Similar to the drift tubes, the particles are
accelerated throughout the structure when the distance between the peak and
the neighboring valley satisfies
L i =
1
2
v i T rf .
In general, linacs can provide beams of high current, and of higher energies than static accelerators, yet because of the single use of each electric
field, they are still rather expensive per MeV. Linacs are frequently used as
pre-accelerators for accelerators of higher energies. They also have the distinctive advantage that they avoid synchrotron radiation, which is often
a limiting factor in circular accelerators for light particles. This aspect is
very important for electron and positron high energy accelerators such as the
Stanford Linear Collider (SLC) at SLAC National Accelerator Laboratory,
California, USA. It is the main reason for the interest in next generation
Linear Colliders, such as plans being considered for an International Linear
Collider (ILC), where a pair of two linacs shoot electrons and positrons at
each other at very high energy.
Recently, linear accelerators have been widely used in producing a free
electron laser (FEL), whose high peak brightness and short pulse duration
has opened up unprecedented opportunities for scientific investigations. Fig.
1.15 shows the setup of the first FEL experiment. Electrons go through a
magnetic device called the undulator, which consists of alternating magnetic
poles. As a result, the trajectory of such an electron is very similar to a sine
function, causing the emitted photon field to add coherently. Together with
the large number of periods, the peak intensity of the X-ray can be orders
of magnitude higher than that from a circular accelerator (see the following
subsection). The advantage of a linac is that it can produce an electron beam
with smaller emittance and shorter pulse duration.
1.3.3 Circular Accelerators
Arguably the simplest circular accelerator is the betatron, which, besides
its practical use as a compact accelerator for lower energies, also represents
an excellent textbook style application of principles of electrodynamics. In
the case of the betatron, the orbit follows a circular shape, which is achieved
by a magnetic field. If the motion is perpendicular to the magnetic field, then
we have in SI units
mv
2
ρ
= qvB, and so ρ =
mv
qB
=
p
qB
,
and so the radius of motion depends only on the momentum and charge of
the particle as well as the magnetic field. Note that the equation is correct
even in the relativistic case, if m is understood to mean the relativistic mass