Beam Rigidity
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Beam Rigidity
In accelerator physics, rigidity is the effect of particular magnetic fields on the motion of the charged particles. It is a measure of the momentum of the particle, and it refers to the fact that a higher momentum particle will have a higher resistance to deflection by a magnetic field. It is defined as ''R'' = ''Bρ'' = ''pc''/''q'', where ''B'' is the magnetic field, ''ρ'' is the gyroradius of the particle due to this field, ''p'' is the particle momentum, ''c'' is the speed of light and ''q'' is its charge. It is frequently referred to as simply "''Bρ''". The unit of the rigidity ''R'' is volts(N·m/C), a convenient unit is GV (''10^9'' V). In this case, unit of ''B'' is T(N·s/C·m), ''ρ'' is in the unit rad/s, ''p'' is in the unit kg· m/s, ''c'' is in the unit m/s, ''q'' is in the unit C. The rigidity is defined by the action of a static magnetic field, whose direction is perpendicular to the velocity vector of the particle. This will cause a force perpendic ...
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Accelerator Physics
Accelerator physics is a branch of applied physics, concerned with designing, building and operating particle accelerators. As such, it can be described as the study of motion, manipulation and observation of relativistic charged particle beams and their interaction with accelerator structures by electromagnetic fields. It is also related to other fields: *Microwave engineering (for acceleration/deflection structures in the radio frequency range). *Optics with an emphasis on geometrical optics (beam focusing and bending) and laser physics (laser-particle interaction). *Computer technology with an emphasis on digital signal processing; e.g., for automated manipulation of the particle beam. *Plasma physics, for the description of intense beams. The experiments conducted with particle accelerators are not regarded as part of accelerator physics, but belong (according to the objectives of the experiments) to, e.g., particle physics, nuclear physics, condensed matter physics or m ...
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Gyroradius
The gyroradius (also known as radius of gyration, Larmor radius or cyclotron radius) is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field. In SI units, the non-relativistic gyroradius is given by :r_ = \frac where m is the mass of the particle, v_ is the component of the velocity perpendicular to the direction of the magnetic field, q is the electric charge of the particle, and B is the strength of the magnetic field. The angular frequency of this circular motion is known as the gyrofrequency, or cyclotron frequency, and can be expressed as :\omega_ = \frac in units of radians/second. Variants It is often useful to give the gyrofrequency a sign with the definition :\omega_ = \frac or express it in units of hertz with :f_ = \frac. For electrons, this frequency can be reduced to :f_ = (2.8\times10^\,\mathrm/\mathrm)\times B. In cgs-units the gyroradius :r_ = \frac and the corresponding gyrofrequency :\omega_ = \frac include a factor ...
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Lorentz Force
In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an electric field and a magnetic field experiences a force of \mathbf = q\,\mathbf + q\,\mathbf \times \mathbf (in SI unitsIn SI units, is measured in teslas (symbol: T). In Gaussian-cgs units, is measured in gauss (symbol: G). See e.g. )The -field is measured in amperes per metre (A/m) in SI units, and in oersteds (Oe) in cgs units. ). It says that the electromagnetic force on a charge is a combination of a force in the direction of the electric field proportional to the magnitude of the field and the quantity of charge, and a force at right angles to the magnetic field and the velocity of the charge, proportional to the magnitude of the field, the charge, and the velocity. Variations on this basic formula describe the magnetic force on ...
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