Post on 20-Dec-2015
The Magnetic Field Profile of New Pole Tips on the
Rutgers 12-inch Cyclotron
John McClain
Robert Friedman
What is a Cyclotron and How Does it Work?
• It’s a “table-top” particle accelerator!
• Accelerates charged particles in circular orbits of increasing radius.
• Essentially a “curled-up” linear accelerator.– The ion accelerates when it passes through an
electric potential.– The increased ion velocity in the presence of
the B-field, leads to an orbit of larger radius.
Cyclotron Chamber
The Dee
Ion Collector
Phosphorescent Screen
Ion Source (cathode)
“Dummy” Dee (grounded)
“Ion” Source
• Hot, negatively biased cathode thermoionically emits electrons.
• Electrons settle into tight orbits about field lines.
• As they travel along the lines, they collide with ambient hydrogen gas, ionizing the atoms
• Free protons are produced!
Beam SpreadingBeam Spreading
• Hydrogen ionized at all points in the electron beam – Initial axial (vertical) amplitude
• Protons have random initial velocities– Uniform magnetic field = Helical path– Small survival rate
Beam Focusing• Small decrease in magnetic field with
increasing radius
• Magnetic field lines are concave inward
• Off of the median plane B-field has a radial, as well as axial, component
Beam Focusing Formalism
• Produces a restoring force on moving charged particles:
n
z )rr
(BB 00
0
0
rznB
Br
r)n(mrmdtd 12 nzmzm
dtd 2
Axial Radial
The n-value is the Thing!
• Can be used to find axial and radial oscillation damping and frequencies
• “The optimum shape of magnetic field in a cyclotron was found to be one in which the n-value rises approximately linearly with radius.”
– Particle Accelerators by Blewett and Livingston
dr
dB
B
rn
Measuring the Field Profile
• Measured field with a Hall Probe fixed to a motorized platform on a track.
• Probe was free to move in the radial direction.
• Reference position w.r.t. the cyclotron center identified by a “bullet” magnet with a sharply peaked profile.
• Made field measurements at stepped positions from the edge to the center of the magnet.
Bullet and Residual Fields
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2 2.5 3 3.5 4
Relative Position (inches)
Fie
ld S
tre
ng
th (
3.3
*T)
Residual Bullet 1 Bullet 2
Residual-Removed Bullet Profile
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.5 1 1.5 2 2.5 3 3.5 4
Relative Position (inches)
Volta
ge D
rop
(V)
Magnet Profile
0
0.2
0.4
0.6
0.8
1
1.2
1.4
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5
Relative Position (inches)
Volta
ge D
rop
(V)
30 Amps 20 Amps 40 Amps
1.01
1.015
1.02
1.025
1.03
0 0.5 1 1.5 2 2.5 3 3.5
0
0.5
1
1.5
2
2.5
3
0 1 2 3 4 5 6
Radius (inches)
n-v
alu
en-value
y = 0.0045x - 0.0014
R2 = 0.9725
0
0.005
0.01
0.015
0.02
0.025
0 0.5 1 1.5 2 2.5 3 3.5