particle accelerator

Examples of particle accelerator in the following topics:

• Examples and Applications

  • A cyclotron is a type of particle accelerator in which charged particles accelerate outwards from the center along a spiral path.
  • The particles are held to a spiral trajectory by a static magnetic field and accelerated by a rapidly varying (radio frequency) electric field.
  • Cyclotrons accelerate charged particle beams using a high frequency alternating voltage which is applied between two "D"-shaped electrodes (also called "dees").
  • The particles accelerated by the cyclotron can be used in particle therapy to treat some types of cancer.
  • Sketch of a particle being accelerated in a cyclotron, and being ejected through a beamline.

• Radiation Detection

  • A radiation detector is a device used to detect, track, or identify high-energy particles.
  • A radiation detector is a device used to detect, track, or identify high-energy particles, such as those produced by nuclear decay, cosmic radiation, and reactions in a particle accelerator.
  • They may be also used to measure other attributes, such as momentum, spin, and charge of the particles.
  • If a particle has enough energy to ionize a gas atom or molecule, the resulting electrons and ions cause a current flow, which can be measured.
  • The pulse yields meaningful information about the particle that originally struck the scintillator.

• Circular Motion

  • Since the magnetic force is always perpendicular to the velocity of a charged particle, the particle will undergo circular motion.
  • Magnetic forces can cause charged particles to move in circular or spiral paths.
  • Particle accelerators keep protons following circular paths with magnetic force.
  • The curved paths of charged particles in magnetic fields are the basis of a number of phenomena and can even be used analytically, such as in a mass spectrometer. shows the path traced by particles in a bubble chamber.
  • The term comes from the name of a cyclic particle accelerator called a cyclotron, showed in .

• Helical Motion

  • In the section on circular motion we described the motion of a charged particle with the magnetic field vector aligned perpendicular to the velocity of the particle.
  • The speed and kinetic energy of the particle remain constant, but the direction is altered at each instant by the perpendicular magnetic force. quickly reviews this situation in the case of a negatively charged particle in a magnetic field directed into the page.
  • The motion of charged particles in magnetic fields are related to such different things as the Aurora Borealis or Aurora Australis (northern and southern lights) and particle accelerators.
  • When a charged particle moves along a magnetic field line into a region where the field becomes stronger, the particle experiences a force that reduces the component of velocity parallel to the field.
  • Describe conditions that lead to the helical motion of a charged particle in the magnetic field

• Overview of Non-Uniform Circular Motion

  • Non-uniform circular motion denotes a change in the speed of a particle moving along a circular path.
  • It follows then that non-uniform circular motion denotes a change in the speed of the particle moving along the circular path.
  • A particle moving at higher speed will need a greater radial force to change direction and vice-versa when the radius of the circular path is constant.
  • The important thing to note here is that, although change in speed of the particle affects radial acceleration, the change in speed is not affected by radial or centripetal force.
  • The corresponding acceleration is called tangential acceleration.

• Radiation Reaction

  • We have found that when a charge is accelerated a certain power is radiated away, so to accelerate the particle we must provide some extra energy to work against a "radiation reaction'' force,
  • We can drop the term from the endpoints if for example the acceleration vanishes at $t=t_1$ and $t=t_2$ or if the acceleration and velocity of the particle are the same at $t=t_1$ and $t=t_2$.We can identify,

• Constant Velocity Produces a Straight-Line

  • There are many cases where a particle may experience no net force.
  • Or there could be two or more forces on the particle that are balanced such that the net force is zero.
  • If the net force on a particle is zero, then the acceleration is necessarily zero from Newton's second law: F=ma.
  • If the acceleration is zero, any velocity the particle has will be maintained indefinitely (or until such time as the net force is no longer zero).
  • Identify conditions required for the particle to move in a straight line in the magnetic field

• Kinetic Energy and Work-Energy Theorem

  • The principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle.
  • The work W done by the net force on a particle equals the change in the particle's kinetic energy KE:
  • where vi and vf are the speeds of the particle before and after the application of force, and m is the particle's mass.
  • The particle is moving with constant acceleration a along a straight line.
  • The relationship between the net force and the acceleration is given by the equation F = ma (Newton's second law), and the particle's displacement d, can be determined from the equation:

• Graphical Interpretation

  • Acceleration is accompanied by a force, as described by Newton's Second Law; the force, as a vector, is the product of the mass of the object being accelerated and the acceleration (vector), or $F=ma$.
  • Because acceleration is velocity in $\displaystyle \frac{m}{s}$ divided by time in s, we can further derive a graph of acceleration from a graph of an object's speed or position.
  • From this graph, we can further derive an acceleration vs time graph.
  • The acceleration graph shows that the object was increasing at a positive constant acceleration during this time.
  • This is depicted as a negative value on the acceleration graph.

• Relationship Between Torque and Angular Acceleration

  • Torque is equal to the moment of inertia times the angular acceleration.
  • Torque and angular acceleration are related by the following formula where is the objects moment of inertia and $\alpha$ is the angular acceleration .
  • If you replace torque with force and rotational inertia with mass and angular acceleration with linear acceleration, you get Newton's Second Law back out.
  • In fact, this equation is Newton's second law applied to a system of particles in rotation about a given axis.
  • Torque, Angular Acceleration, and the Role of the Church in the French Revolution