Accelerators Flashcards
Linacs
Explain the basic principle of operation of a linear accelerator (linac).
A linear accelerator (linac) is comprised of a succession of drift tubes (= Faraday cages) with holes at their ends so that the particles can enter and exit. The drift tubes are arranged in a sequence with a passage through their middle for the particles to pass. There are gaps between the tubes whose fields accelerate the particles.
- potential of the tubes may vary when particles are inside w/o changing their energy
- acceleration happens when charged particle is subjected to a field: particles receive a push every time they enter a new section of the accelerator
- tube length increases with speed: the time it takes for a particle to travel from one drift tube to the next must match the oscillation period of the RF fields
- idea: the presence of the accelerating field is enough at the location of the particle: well-timed pulses (several separate smaller tubes)
- The field inside the Faraday cage is not affected by the potential outside.
- The electric field accelerates the particles, not the potential.
Linacs
How does a linac differ
from a circular accelerator?
Circular accelerators:
- particles on circular path
- uses magnetic field to bend path: strong magnets needed
- synchrotron radiation plays a role
- particles can gain higher energies over many loops
Acceleration is achived by electric fields here as well.
Linacs
What are the main limitations of electrostatic accelerators like the Van de Graaff type accelerator? How do RF linacs overcome these limitations?
Limitations of electrostatic accelerators:
- size of potential difference that can be kept (hard to maintain the high-voltage supply)
- negatively charged ions are needed (sometimes difficult to produce)
- generally work only for ions with one extra electron
- large size needed for larger energies which is impractical from a certain point: only low frequencies used
Advantages of RF linacs:
- particles accelerated have positive charge
- oscillating electric fields for acceleration: alternating high frequency (180 degrees while the particle passes from one gap to another, through the electrode), no continous high voltage needed
- continuous acceleration with each cycle of the RF field: higher energy achievable
180 degree change = polarity of voltage reversing
In RF linacs acceleration voltage can be applied several times.
Linacs
What practical challenges
arise when increasing the voltage?
- At higher frequencies tubes radiate like antennas
- At very high voltages, the air around the components can ionize, leading to corona discharge: energy loss, potential damage to components (proper vacuum conditions and insulation are required)
- More power needs to be generated, which is inefficient at high frequencies: RF fields must be scaled appropriately
Linacs
Why do modern linacs often use superconducting cavities? What are the advantages and challenges associated with superconducting RF technology?
Because they generate a stronger electric field, making it possible to accelerate particles to higher energies.
Advantages:
- higher energy achievable
- more efficient operation at higher frequencies
- at RF the resistance is ~5 orders of magnitude lower than copper (microwave surface resistance), so there’s less power lost due to the zero resistivity at low temp.
Challenges:
- as the voltage oscillates, the particle must pass through the cavity at the right time
- cryogenic temperatures required for the superconductors
An RF accelerating cavity is a metal chamber in which electromagnetic waves generate an electrical field.
Linacs
In a RF quadrupole (RFQ), what is the purpose of the modulated electrode structure? How does it both focus and accelerate the beam?
The purpose is that the RFQ can acclerate the particles in the appropriate phase.
Focusing: the transverse quadrupole electric field focuses in one plane and defocuses in the other
Accelerating: the alternating longitudinal component of the electric field accelerates the particles in the appropriate phase
- longitudinal electrode modulation: 180 degree diff. between x and y electrodes
Early particles feel a stronger kick, late one a weaker one, so keeping the phase is important.
Circular accelerators
How do cyclotrons work in general?
The particles accelerate on a circular path in a constant magnetic field created by two large magnets (one on top, one on bottom). The magnetic fields bends their path and the electric field at the gap between the two D-electrodes accelerate at every pass.
- increasing energy = increasing cyclotron radius
- cyclotron frequency: the RF between the dees (when the particle turns around)
- continuous acceleration
- limit in energy: due to relativistic effects particles become more massive and the cyclotron frequency falls out of synch w/ the accelerating RF
Circular accelerators
How is focusing implemented in cyclotrons?
The horizontal component of the magnetic field focuses the particles vertically, towards the inside where the magnetic field is stronger.
At the boundary of the air and the iron magnets, the field is perpendicular to the surface of the magnet. The further away the magnetic iron yokes are, the weaker the magnetic field.
- the field that focuses vertically gets weaker as we move outwards, therefore the focusing decreases
If the field got stronger outwards, it would defocus vertically.
Circular accelerators
What’s the relativistic limitation of cyclotrons and how do they bypass it?
Due to relativistic effects particles become more massive and the cyclotron frequency (and with it the particles) falls out of synch w/ the accelerating RF.
- as the radius increases so does the momentum but the speed saturates
Solutions:
- synchro-cyclotron: decreasing B field —» vertical focusing —» decreasing the RF as the energy increases to match the particles’ mass-dependent cyclotron frequency
- provides particles bursts
- low beam intensity due to bunching
- huge magnet of large radius
- isochronous cyclotron: increasing B field to larger radii to keep orbit frequency constant —» vertical defocusing —» edge focusing
- changing profile, nonvertical B: Lorentz force keeps particles on track
- very high maximum achievable extracted proton current
Circular accelerators
What are betatrons?
They use the electric field induced by a varying magnetic field to accelerate electrons.
- fixed electron orbit
- beam is kept together by weak focusing
Circular accelerators
What’s the working principle of synchrotrons?
The accelerations happens in the electric field of a resonator (cyclotron-shape with gaps). The RF and magnetic field are increased with time such that the orbit radius is constant.
- enough to create a magnetic field along the circulat orbit
- particle not participating in collisions can be reused
- periodic arrangement: focus (quadrupole), drift (straight section), defocus (dipole), drift (these sections repeat)
- separate corrector magnets (sextupole)
quadrupole = two dipoles w/ diff profiles
- So different magnets play the role of deflection (dipole) and focusing (quadrupole).
- FODO: F —» focus vertically, defocus horizontally, D —» defocus vertically, focus horizontally
Circular accelerators
How does beam focusing work in synchrotrons?
Accelerating particles radiate energy in discreet quanta, meaning radiation increases the beam size, so the beam needs to be focused.
Weak focusing: a dipole magnet’s uniform magnetic field keeps the particles in a circular path
- focuses vertically with the effect of the Lorentz force
Strong focusing: focusing and defocusing after each other gives net focusing, which can be much stronger —» net focusing
- quadrupole magnets defocus from the north magnet and focus on the east —» optical analogy
- magnets don’t have to focus in both directions at the same time
- provides much smaller sized beams
- no need for huge vacuum pipes and magnets
Main components of accelerators
What are the different types of magnets employed in accelerators?
Dipole magnets: keeping the particle beam on a circular path
- “cosθ” dipole magnets: strange distribution for the current, for better quality magnetic fields
Quadrupole magnets: focusing the beam
Sextupole magnets: correcting path of particles with non-nominal momentum
Multipole magnets: improving the magnetic field (dipole field) at the edges of the dipole so that the field is as homogenous as possible
Main components of accelerators
Why do we need two vacuum tubes?
Because there are two beams.
- same charged particles: two are needed to keep them on track, they go in the same direction and meet only at the meeting point
- particle-antiparticle pairs: the same magnetic field can be used
Main components of accelerators
Why do we need superconducting cables? What is quenching in this case?
Because shorter, thinner cables are enough if they’re superconducting.
- quenching is the loss of superconductivity
Production of particle beams
How can we produce particle beams? What types of beams are there?
Types of beams:
- primary beam: direct production
- secondary beam: a primary particle beam hits a target and creates the secondary particles
Types of particles:
- electrons: electron gun (thermic cathode, laser-driven semiconductor photocathode)
- positrons: EM interaction of a photon or electron with an atomic nucleus followed by electron-positron pair production, nuclear β+ decay
- protons: breakup of H2, then ionizing atoms
- ions: gas ionization
- anti-protons, pions, kaons, muons, neutrinos: proton beam fired to a target, selecting from many particles
Production of particle beams
How can we produce ion beams?
A low pressure gas or plasma is ionized usually by electrons.
- E(kin) > ionization energy (E(kin) ~ 2-3I(n) is optimal)
- electrons and the plasma have to be closed in and be kept alive with stable parameters
- multiply charged ions: many collisions and trapping for a long time needed to remove several electrons
- electron sources: external source (electron plasma), ionized plasma
Production of particle beams
What are the similarities and differences between the Penning ionization gauge (PIG) ions source, the duoplasmatron and the electron cyclotron resonance ion source (ECRIS)? When do we use them?
PIG ion source: good for low-charge-state ions
- electron source: heated cathode
- Penning trap: electrons are trapped in the longitudinal direction by E field, in the the transversal direction by B field, ionizing a low-pressure gas
- system on positive potential
- puller/extraction electrodes on ground potential: accelerating the ions
- used in vacuum gauges, basic plasma research
Duoplasmatron: good for low-charge-state ions
- provides higher ion currents
- electron source: heated cathode
- hydrogen plasma is ionized due to continuous electron inflow
- first acceleration stage located already inside the particle source
- used in particle accelerators and medical applications
ECRIS: good for highly charged ions
- resonance: applying the electric field at the constant cyclotron frequency for a given B, the electrons gain more and more energy, moving in a larger and larger radius, they become capable of ionization
- resonant transfer of energy from the electric field to the electron occurs
- constant acceleration «— electron sees a constant E field because of the matching frequencies
- trapping with two or three coil along the longitudinal axis, sextupole field in the radial direction
- in inhomogenous magnetic fields the resonande condition is valid only locally: ECR zone (resonance only happens here)
- used in fusion research, high-energy physics and heavy-ion accelerators
- If the pressure is too high, the electrons collide too often, and cannot gain enough energy for the ionization, if the pressure is too small, the electrons do not collide often enough, there is no ionization.
- In duoplasmatrons electrons, as well as protons are flowing.
- Magnetic mirror: in stronger magnetic fields the field lines are converging. If the angle of the particles is too small, they escpae from the bottle.
Production of particle beams
What is beam cooling? Why is it needed? What methods
can be used?
The particles of a beam being hot means that their energy, potision and direction are widely different; cooling means make them similar. This is necessary because a hot beam has difficulty staying in the beam pipe, diffuse and is not bright enough.
Stochastic cooling: removes randomness
- addressing individual particles within each bunch using electromagnetic radiation: optical scanner detects the position of individual particles
- kicker magnets: dipole magnets rapidly switch particles’ trajectory between two paths
- “stochastic”: only average properties can be addressed, so the kick applies only to small groups —» multiple steps are required to cool the beam
- the smaller the group of particles which can be detected and adjusted at once (requiring higher bandwidth), the faster the cooling —» bunches are as short as possible in the accelerators of the ring and as long as possible in the coolers
Electron cooling:
- beam of dense quasi-monoenergetic electrons produced and merged with the ion beam: electrons’ velocity made equal to that of the ions
- ions Coulomb scatter in the electron “gas”: exchange of momentum with the electrons
- same momentum of electrons and ions: thermal equilibrium is reached —» thermal energy is transferred from the ions to
the electrons, the beam is cooled
- The strength of the kick must be accurately matched to the momentum of the particle by the power modulator.
- Lastly, the electron beam is bent away from the ion beam.
Beam parameters
What is beam emittance?
It measures the average spread of particle coordinates in position-and-momentum phase space (Δp is a function of z).
- so it measures the beam distribution and how quickly it changes in the longitudinal direction
- normalized emittance: ε(N) = εγ = constant, where ε is the geometrical emittance
Normalized emittance is reqiored because when we accelerate beams we give them momentum only in the longitudinal direction.
Beam parameters
What is the parameter β(star) refering to?
It is the amplitude function determined by magnet configuration (especially quadrupole arrangement) and powering: β=π·σ²/𝜀.
- σ: beam width, 𝜀: transverse emittance
- unit = length
- lower β: narrower (“squeezed”) beam, higher β: wider (straight) beam
Sometimes it’s referred as the distance from the focus point to the point where the beam is twice as wide.
Beam parameters
What is luminosity? How can it be measured?
It’s a characteristic of the accelerator, it describes the interaction rate: R = dN/dt = σ · L, where L is the luminosity and σ is the cross section.
- single bunch instantaneous luminosity (SBIL): L = f(orbit)N1N2/(4π σx σy)
- instantaneous luminosity: sum of SBIL for all bunch pairs if bunches are uniform, L = f(orbit) n(bunch/beam) N² / (4π σx σy)
- for high luminosity: high population bunches, high bunch current, low emittance low β(star)
- measurement: luminometers (measures rate proportionality to luminosity), with well-known precisely calculable physical processes in lepton colliders, from measuring the accelerator beam parameters in hadron colliders
