Experimental Study of Dispersion Control Utilizing Both Magnetic
and Electric Fields
Mikio Tanabe1, Masahiro Ikegami1, Akira Noda1, Toshiyuki Shirai1, Hiromu Tongu1, Hikaru Souda1, Shinji Shibuya2, Koji Noda2
ICR, Kyoto University 1
National Institute of Radiological Sciences 2
COOL05September 18th - 23th,2005
Galena, Illinois
Table of Contents
1. Motivation• ‘S-LSR’ and cooling experiments• Why and how?2. Electrodes to Control Dispersion• Design and electric field3. Experiments• Controlled linear dispersion4. Summary and Future Plans
Ion Storage Ring ‘S-LSR’
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
S-LSR (under construction)
H-typeBending Magnet
1.05mBending radius
QM-BM-QMLattice
6Superperiodicity
22.557mCircumference
24Mg+ : 35keV
12C 6+ : 24MeV
Proton : 7MeVStored beam
(plan)
Parameters
Cooling Experiment
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
Electron cooler Proton Ring dye laser Mg+
Aim of our LASER cooling
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
Models of Ordering beams
To realize ordering or crystallized beam
What is ordering or crystallized beam ?
Each particle keeps about the same relative position
Issue in storing ordered beam
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
Ordering particles at a bending section
Shearing force want to be canceled
less timemore time
How to overcome ‘Shearing force’
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
Same angular velocity
Decelerated
AcceleratedAccelerated
Decelerated
Same velocity
Lines of electric force
Potentials are adjusted
Example: Uniform electric field strength
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
EB
Bending magnet
Outer main electrode(negatively biased)
Coil
EB
EB
60
Center of the curvature ( r = 0)
Inner main electrode(positively biased)
Reference orbit
qEqvBrvm −=
2
2
2
11
111−−−
⎟⎠⎞
⎜⎝⎛ ∆+−⎟
⎠⎞
⎜⎝⎛ ∆+=⎟
⎠⎞
⎜⎝⎛ ∆+
vv
vqE
vv
vqB
rr
rm
( )EvBvv
mvqr
rr 22 −
∆=
∆
Equation of motion
When , vvv ∆+→
Neglecting 2nd or higher order,
02 =− EvBCondition to cancel linear dispersion
Table of Contents
1. Motivation• ‘S-LSR’ and cooling experiments• Why and how?2. Electrodes to Control Dispersion• Design and electric field3. Experiments• Controlled linear dispersion4. Summary and Future Plans
Conditions at electrodes set point
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
Bending magnet of S-LSR Cross section of the magnet
Vacuum ductElectrodes
Movable
Structure of a set of electrodes
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
Intermediate electrode
30mm
26mm
Main electrode
Main electrode
Cross sectional view
3-d view
Picture of a set of electrodes
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
26mm
30mm
1082 mm
Hole for laser path
Electric field precision
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
Voltages given each electrode [V]
(optimized for 35keV 24Mg+)
Errors from E=k/r
near the reference orbit
1007 -993
560
183
-180
-556
Table of Contents
1. Motivation• ‘S-LSR’ and cooling experiments• Why and how?2. Electrodes to Control Dispersion• Design and electric field3. Experiments• Controlled linear dispersion4. Summary and Future Plans
Experimental setup
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
Setup from an ion source to fluorescent screen
Fluorescent screen
1000mm
Ion source
Beam slit
Experimental condition
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
• Beam : N2+
• Energy : 25 keV• Emittance : 5π mm mrad• Vacuum condition : ~10-5Pa• Magnetic and Electric field strength
Ex.)5.71×1040.252
3.81×104
4.76×104
NoneE[V/m]
Ex.)0.2050.230
Only B0.115B [T]
EvB 2>
EvB 2<EvB 2= Dispersion free
Images on screen 1
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
Magnetic field only
Outside
increase
Inside
decreaser∆
keV (beam kinetic energy)
Images on screen 2
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
Magnetic and electric field (dispersion cancel condition)
Outside
increase
Inside
decreaser∆
keV (beam kinetic energy)
Results 1
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
Magnetic field onlyMagnetic and electric field
(dispersion cancel condition)
Linear dispersion is canceledMomentum deviation (%)
Deviation of radial position
(%)
Momentum deviation (%)
rr /∆
vv /∆ vv /∆
Results 2
COOL05, 19-23 Sep. 2005 @Eagle Ridge Resort and Spa, Galena Illinois, The United States
Dispersions are controlled
vB :E=2.7:1 vB :E=2.3:1
EvB 2>
vB :E=1.8:1 vB :E=1.7:1
EvB 2<
Momentum deviation (%)
Deviation of radial position
(%)
vv /∆
vv /∆ vv /∆
rr /∆
rr /∆ rr /∆
rr /∆
Summery and Future Plans
1. Design a set of Electrodes • Field error<0.1% (+-5mm from the reference orbit)
2. Test the effect of electric fields• Canceled linear dispersion• Controlled linear dispersion (from + to )
1. Apply dispersion control to storage ring
2. Apply these dispersion control to laser cooling
Summery
Future−
