Particle Accelerators Flashcards
What were the early methods of particle acceleration, and what were their limitations?
Early accelerators, such as the van de Graaff generator and Cockcroft-Walton generator, used high voltages to accelerate particles up to a few MeV. However, these methods were limited in their ability to achieve higher energies.
Explain the basic equations governing relativistic energy, momentum, and motion of particles in accelerators.
Relativistic energy
E is given by
E=mγc^2, where
m is the rest mass and γ is the Lorentz factor.
Relativistic momentum
p is given by
p= mγv.
The relationship between energy and momentum is
E^2 = p^2 c^2 +m^2 c^4
The Lorentz force
F acting on a particle in an electromagnetic field is given by
F=dp/dt=q(E+v×B).
How do linear accelerators (LINACs) work, and what are their advantages and limitations?
Linear accelerators use a series of cylindrical electrodes called drift tubes to accelerate particles in a straight line. They are advantageous for not requiring expensive magnets and for avoiding energy loss from synchrotron radiation. However, they require many structures and are limited in achieving high energies due to voltage breakdown issues.
Describe the principle and operation of the cyclotron.
The cyclotron bends particles into circular paths using a magnetic field and applies an alternating electric field across semi-circular chambers called “dees”. The particles orbit inside the dees and accelerate each time they pass through the gap between them. The cyclotron frequency is independent of the radius due to the compensation between gain in orbit length and gain in velocity.
What is a synchrotron, and how does it address the limitations of conventional cyclotrons?
A synchrotron varies both the magnetic field and the resonant frequency to allow particles to orbit at nearly constant radius, requiring a ring-shaped magnet. This allows for higher energies to be achieved compared to conventional cyclotrons by compensating for relativistic effects.
