Transcript The Magnetic Field Profile of New Pole Tips on the Rutgers
The Magnetic Field Profile of New Pole Tips on the Rutgers 12-inch Cyclotron John McClain Robert Friedman
Cyclotron
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.
Basic Cyclotron Design
F
qv
B
ma
qvB
mv
2
r
r
mv qB T
2
r v
2
m qB
qB m
Rutgers 12-inch Cyclotron
Solenoid Coils Hydrogen Pole Tip Instruments and Controls Cyclotron Chamber
Cyclotron Chamber The Dee Ion Collector Phosphorescent Screen Ion Source (cathode) “Dummy” Dee (grounded)
Chamber Reloaded
“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 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
Sloped Pole Piece
Beam Focusing Formalism • Produces a restoring force on moving charged particles: Axial
B z
B
0
( r
0
r ) n
Radial
B r
nB
0
z r
0
d dt
m
2
nz d dt
m
r
m
2
(
1
n )
r
The n-value is the Thing!
n
r B dB dr
• 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
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.
0.6
0.5
0.4
1 0.9
0.8
0.7
0.3
0.2
0.1
0 0 Bullet and Residual Fields 0.5
1 1.5
2 2.5
Relative Position (inches)
Residual Bullet 1 Bullet 2 3 3.5
4
Residual-Removed Bullet Profile 0.4
0.3
0.2
0.1
0 0 0.9
0.8
0.7
0.6
0.5
0.5
1 1.5
2 2.5
Relative Position (inches) 3 3.5
4
Magnet Profile 1.4
1.2
1 0.8
1.03
0.6
1.025
1.02
0.4
1.015
0.2
1.01
0 0.5
1 1.5
2 2.5
3 3.5
0 -0.5
0 0.5
1 1.5
2 2.5
3 3.5
4 4.5
5 5.5
Relative Position (inches)
6 30 Amps 20 Amps 6.5
40 Amps 7 7.5
8 8.5
9 9.5
n-value
3 2.5
2 1.5
1 0.5
0 0 0.025
0.02
0.015
0.01
0.005
0 0
y = 0.0045x - 0.0014
R
0.5
1
2 = 0.9725
1.5
2 2.5
3 3.5
1 2 3 Radius (inches) 4 5 6