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

qB

mvr

r

mvqvB

maBqvF

2

qB

m

v

rT

22

m

qB

Rutgers 12-inch Cyclotron

Instrumentsand Controls

CyclotronChamber

Pole Tip

Hydrogen

Solenoid Coils

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 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

Sloped Pole Piece

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

The End