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Nuclear and Particle Physics2 (Linac (Drift tube linear accelerator is…
Nuclear and Particle Physics2
Red = Proton
Blue = Electron
Magnetic Field into page
Vq = 1/2mv^2 --> v = sqrt(2Vq/m)
r = p/Bq --> r = mv/Bq --> r = (m * sqrt((2Vq/m)/Bq)
rBq = m(sqrt((2Vq)/m) --> (r^2 * B^2 * q^2) = m^2 = (2Vq/m)
Rearrange for m
Linac
Drift tube linear accelerator is composed of a series of drift tubes which are alternately connected to AC power supply
The length of drift tubes increases as you go down further along the accelerator
Why is there a vacuum
To avoid collisions with air molecules --> this would scatter electron beam
Where is the electric field
There is p.d. in gaps between tubes as tubes are connected to alternating parts of alternating voltage. Field is between tubes
Why are they called drift tubes
Particle don't accelerate within tubes; they drift
Where is the electric field 0?
Inside tube. They have high voltage supplied but no p.d.
Whilst in tubes, voltage switches ( + > - > +)
Why do tubes get longer
Time spent in tube must be constant across tubes so that frequency of supply (and alternation of voltage) is constant
Cyclotron
Why is proton rotated clockwise?
Fleming's Left Hand Rule. Resultant force acts towards center of circle
Why use a magnetic field?
It doesn't speed up particles because magnetic force is |_ to direction of travel --> No component of force acting on path of proton . Magnetic field keeps rotational path
How are high energies achieved
Alternating current = Alternating voltage.
When proton reaches the gap, the opposite Dee is negative and proton is accelerated by p.d. provides energy Vq)
Hz of supply = Hz of rotations around Dee
Final Ek = 2 * Vq * Norbits
F = Bq / m *2* pi
Beam experiences a |_ force from B-field
F = mv^2 / r = Bqv
r = mv/Bq
Leaving a path radius that increases linearly with speed. Time for each circuit
T=(2 x pi x r)/v == (2 x pi x m x v)/Bqv
Frequency of alternating p.d. is constant as it must switch direction exactly when the particle exists from 1 Dee across gap
Relativity
When a particle approached the speed of light, its mass increases
Einstein's Theory of Relativity
As per f = Bq/m2pi, the frequency of orbits would be out from the frequency of supply
Accelerator will not work properly
Synchro-cycltron lowers frequency of supple in sync with orbital frequency of particles
Relativistic Effect
