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1. Particle Accelerators-Lecture 2
Fayoum University
Faculty of Science
Physics Department
Prepared and Presented by
Dr. Mohammed Attia Mahmoud
- PhD from Fayoum University, Egypt and Antwerp university Belgium
- Member in Egyptian network for High Energy Physics
- Researcher in CMS experiment in CERN, Geneva

2. 1. Frontiers in accelerator physics and technology research
2. Historical Developments
3. Natural Accelerators
4. Electrostatic Accelerators
5. Induction Accelerators
A: Induction linac
B: Betatron
Outlines

3. The physics and technology of accelerators and storage rings involves many branches
of science. These include electromagnetism, solid-state properties of materials, atomic
physics, superconductivity, nonlinear mechanics, spin dynamics, plasma physics, and
quantum physics.
Frontiers in accelerator physics and technology research
Since higher energy leads to new discoveries, and higher luminosity leads to higher precision
in experimental results, Some of frontiers topics in beam physics are as follows.
•High energy: For high energy hadron accelerators such as the Tevatron at Fermilab, the
Large Hadron Collider (LHC) at CERN, and the contemplated Very Large Hadron Collider
(VLHC), high-field superconducting magnets and the stability of high-brightness beams are
important issues. For lepton colliders, high acceleration gradient structures, wakefields, and
high power rf sources are important. Some proposed e+
e-
colliders are the Next Linear Collider
(NLC), the Japan Linear Collider (JLC), the CERN Linear Collider (CLIC), and the TeV
Superconducting Linear Accelerator (TESLA).
•High luminosity: To provide a detailed understanding of CP violation and other
fundamental symmetry principles of interactions, dedicated meson factories such as the $-
factory at Frascati National Laboratory in Italy and the B-factories at SLAC and Cornell in the
U.S. and at KEK in Japan were built in the 1990's, and the Tau-Charm factory is being
contemplated in Beijing, China. a high-intensity proton source can be used to drive secondary
beams such as kaons, pions, and muons.

4. •High-brightness beams: Beam-cooling techniques have been extensively used in
attaining high-brightness hadron beams. Stochastic cooling has been successfully applied to
accumulate anti-protons. This led to the discovery of W and Z bosons, and b and t quarks.
Electron cooling and laser cooling have been applied to many low energy storage rings used in
atomic and nuclear physics research. Ionization cooling is needed for muon beams in μ+
μ-
colliders.
•Accelerator applications: The medical use of accelerators for radiation treatment,
isotope production, sterilization of medical tools, etc., requires safety, reliability, and ease in
operation. Higher beam power density with minimum beam loss can optimize safety in
industrial applications such as ion implantation, electron-beam welding, material testing, food
sterilization, etc.
Historical Developments
A charged particle with charge q and velocity v in the electromagnetic fields (E, B) is exerted by
the Lorentz's force F:
The charge particle can only gain or lose its energy by its interaction with the electric field E.

5. where m and p = mv are the mass and momentum of the particle. The momentum rigidity
of the charged particle is
when the magnetic flux density is perpendicular to v, the bending radius is
Accelerators are composed of ion sources, cavity and magnet components that can generate
and maintain electromagnetic fields for beam acceleration and manipulation, devices to detect
beam motion, high vacuum components for attaining excellent beam lifetime, undulators and
wigglers to produce high brilliance photon beam, targets for producing secondary beams, etc.
where Bρ is measured in Tesla-meter, and the momentum is measured in GeV/c per amu.
Accelerators can be classified as linear or circular, electrostatic or radio frequency, continuous
(CW, DC or coasting beam) or bunched and pulsed. They are designed to accelerate electrons
(leptons) or hadrons, stable or radioactive ions. Accelerators are classified as follows, in no
specific chronological order.

6. Natural Accelerators
A- Radioactive accelerators
In 1911, Rutherford employed a particles escaping the Coulomb barrier of Ra and Th nuclei
to investigate the inner structure of atoms.
B- Cosmic rays
Cosmic rays arise from galactic source accelerators. Nuclei range from n and H to Ni; heavy
elements have been measured with energies up to 3 x 1020
eV. Muons were discovered in
cosmic-ray emulsion experiments in 1936 by CD. Anderson, S.H. Neddermeyer, and others.
Pions were discovered in 1947 in emulsion experiments. Interest in the relativistic heavy ion
collider (RHIC) was amplified by the cosmic ray emulsion experiments.

7. Van de Graaff and tandam accelerators:
In 1931, R.J. Van de Graaff developed the electrostatic
charging accelerator.9 In the Van de Graaff accelerator, the
rectifier units are replaced by an electrostatic charging belt,
and the high-voltage terminal and the acceleration tube are
placed in a common tank with compressed gas for
insulation, which increases the peak acceleration voltage.
Today the voltage attained in tandem accelerators is about
25 MV.  Electron accelerator.
A motor driven belt runs inside the column, and a high voltage
power supply mounted in the base sprays charge onto the belt as it
passes by.
The charge is removed by sharp Corona needles and uniformly
distributes over the surface of the sphere.
Video
Electrostatic Accelerators
X-ray tubes
William David Coolidge in 1926 achieved 900-keV electron
beam energy by using three X-ray tubes in series. The
cascade type of X-ray tube is called the Coolidge
tubes.

8. Cockcroft-Walton electrostatic accelerator
In 1930, John Douglas Cockcroft and Ernst Thomas Sinton Walton
developed a high voltage source by using high-voltage rectifier
units. In 1932, they reached 400-kV terminal voltage to achieve
the first man-made nuclear transmutation: p + Li —>2 He. The
maximum achievable voltage was limited to about 1 MV because
of sparking in air.
This accelerator is a cascade generator consisting of identical
stages containing capacitors and rectifiers. The secondary
winding of a transformer supplies an alternating voltage to the
first stage. Each stage is a voltage doubling circuit. Because of
the rectifiers that conduct only if the anode voltage is greater
than the cathode voltage, the voltage at point P1 varies
between 0 and 2V and the voltage at P2 is constant and equal
to 2V. If the cascade generator consists of n identical stages, a
constant voltage 2nV is generated at the output in the absence
of any load.

9. 1.3 Induction Accelerators
According to Faraday's law of induction, when the magnetic flux changes, the induction
electric field along a beam path is given by
ɛ is the induced electric field, ф is the total magnetic flux, ds is the differential
for the line integral that surrounds the surface area, dS is the differential for the and B is
the "magnetic field“ enclosed by the contour C.
A: Induction linac
The induction linac was invented by N.C. Christofilos in the 50's for the
acceleration of high-intensity beams. A linear induction accelerator (LIA) employs
a ferrite core arranged in a cylindrically symmetric configuration to produce an
inductive load to a voltage gap. Each LIA module can be viewed as a low-Q 1:1
pulse transformer. When an external current source is discharged through the
circuit, the electric field at the voltage gap along the beam axis is used to
accelerate the beam. A properly pulsed stack of LIA modules can be used to
accelerate high-intensity short-pulse beams with a gradient of about 1 MeV/m
and a power efficiency of about 50%.

10. B: Betatron
The induced electric field along the beam axis is given, according to Faraday's law of induction
Bav is the average magnetic flux density inside the circumference of the beam radius. The
final particle momentum
The betatron, which is used to accelerate electrons.
In all the accelerators we have considered so far, the magnetic field remains constant and the
radius of the particle trajectory increases with energy. In the betatron, on the other hand,
the magnetic field is increased as the particles accelerate so that the circular path remains
the same size. The accelerating electric field arises naturally from the magnetic field, which is
changing very rapidly with time, in accordance with the law of induction. It is therefore not
necessary to construct a special accelerating section.

11. 11
Betatron, principle of operation
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12. The Betatron principle that the guide field Bg is equal to 1/2 of the average field Bav
In order for the orbit radius to remain constant, there must exist definite relation, called the
Betatron condition, between the rate of energy increase, which is determined by
the change in the field in the central part, and the rate of increase of the magnetic guide
field. The relation reduces to the condition.
In 1940 D. Kerst was the first to operate a Betatron to achieve 2.3 MeV. In 1949 he
constructed a 315-MeV betatron16 at the University of Chicago with the parameters p = 1.22
m, B% = 9.2 kG, Einj = 80 - 135 keV, /inj = 13 A. The magnet weighed about 275 tons and the
repetition rate was about 6 Hz.

13. 1.4 Radio-Frequency (RF) Accelerators
It is difficult to attain very high voltage in a single acceleration gap. It would be more
economical to make the charged particles pass through the acceleration gap many times.
This concept leads to many different rf accelerators,17 which can
A. LINAC