RF Cavities and Forces on Particles
RF Cavities and Particle Accelerators Particle
accelerators use RF cavities to ramp up the velocity of particles. I
believe the particles ride on the negative or positive parts the RF
waves depending on whether the charge is + or - The questions I have are:
1. Is there a relationship between the force the particle feels and
the intensity of the rf wave the particle is "attached" to while
riding the wave?
2. Is the velocity of the particle determined by the RF frequency or
the speed at which the rf wave is travelling (i.e that of light)?
3. I am hoping there is some sort of simple mathematical
relationship that describes the force the particle feels in relation
to its velocity, Rf frequency, rf field intensity and where the
particle is at any given moment of time?
Actually, your questions ARE pretty simple, but there might be a
slight misconception lurking under there. So I will proceed with some caution.
1. A charged particle "perceives" an electromagnetic wave as
traveling and oscillating electric and magnetic fields. The force
on a charged particle from an electric field is simply the
particle's charge multiplied by the field (which, being a vector,
has a direction as well as intensity). The force from a magnetic
field is a bit more complicated, as it depends on the relative
velocities of the particle and field as well as on the charge and
field intensity, but basically again it is proportional to the field
strength and the charge.
2. Neither. The velocity of the particle depends on what the
velocity was a short time ago and on the force. This is because
force determines acceleration, not velocity. Acceleration is the
RATE of CHANGE of velocity, which is quite different from velocity
(though of course acceleration and velocity are obviously
related). This is Newton's second law, which states that the
acceleration of any body is directly proportional to the sum of all
forces acting on the body and inversely proportional to its mass, a
= F/m. (At the very high speeds attained by particles in
accelerators, there is a substantial relativistic correction to this
formula, but the idea that force determines acceleration, not
velocity directly, still stands.)
3. Force formulas: For a particle of charge q in an electric field
E, the force on the particle is qE. For a particle of charge q
moving at velocity v relative to a magnetic field B, the force on
the particle is qv x B, where "x" denotes the vector cross
product. (In English, the force is perpendicular to both v and B,
and has a magnitude qvB sin(theta), where theta is the angle between
the "electric momentum" qv and the magnetic field B.
Richard E. Barrans Jr., Ph.D., M.Ed.
Department of Physics and Astronomy
University of Wyoming
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Update: June 2012