Transcript isac - titan

Simulation and Off-line Testing
of a Square-wave-driven RFQ
Cooler and Buncher for TITAN
Mathew Smith: UBC/TRIUMF
ISAC Seminar 2005
Overview
The TITAN project
The need for a cooler and buncher
Square-wave vs sine-wave
Simulations
RFQ test stand
Experimental setup and status
Summary and outlook
ISAC
ion beam
RFQ
cooler &
buncher
EBIT
charge
breeder
Magnetron motion, ω-, due to
magnetic field
Axial motion, ωz, due to
application of an electrostatic
harmonic potential
Reduced cyclotron motion,
ω+, due to coupling of ions
magnetic moment to the
electric field
    
2
c
2

2

q
c  B
m
2
z
m/q
selection
Penning
trap
B
z
U0

axial (z)
magnetron (-)
cyclotron (+)
ISAC
ion beam
RFQ
cooler &
buncher
EBIT
charge
breeder
m/q
selection
Penning
trap
B
Dipole excitation prepares
ions in pure ω- state
Application of quadrupolar
excitation couples ω- to ω+.
  
Extracting ions through
magnetic field converts radial
energy into longitudinal
energy
Ion time of flight spectrum
can be used to obtain ωc.
z
TRAP
DRIFT TUBE
MCP
ISAC
ion beam
RFQ
cooler &
buncher
EBIT
charge
breeder
ISOLTRAP:
t1/2 = 1 s, δm/m = 1x10-8
t1/2 = 50 ms, δm/m = 5x10-8
m/q
selection
Penning
trap
δm

m
q
m
N TB
m = 100 u, N = 10, 000
2x10-7
1x10-7
-8
5x10
B = 4 T, q = 1
B = 6 T, q = 1
B = 9.4 T, q = 1
-8
dm
m
2x10
-8
1x10
5x10-9
-9
2x10
-9
1x10
0.05 0.07
0.01 0.015 0.02 0.03
Observation Time (s)
0.1
ISAC
ion beam
RFQ
cooler &
buncher
EBIT
charge
breeder
TITAN:
t1/2 = 50 ms, δm/m = 1x10-8
m/q
selection
Penning
trap
δm

m
q
m
N TB
m = 100 u, N = 10, 000
2x10-7
1x10-7
-8
5x10
B = 4 T, q = 1
B = 6 T, q = 1
B = 9.4 T, q = 1
-8
dm
m
2x10
-8
1x10
5x10-9
B = 4 T, q = 10
-9
2x10
-9
1x10
B = 4 T, q = 20
B = 4 T, q = 30
B = 4 T, q = 50
0.05 0.07
0.01 0.015 0.02 0.03
Observation Time (s)
0.1
ISAC
ion beam
RFQ
cooler &
buncher
EBIT
charge
breeder
m/q
selection
Motivation for mass measurements
Three areas where TITAN can contribute:
Weak interaction studies
Atomic and Nuclear Mass Models
Stellar Nucleosynthesis
Penning
trap
ISAC
ion beam
RFQ
cooler &
buncher
EBIT
charge
breeder
m/q
selection
Penning
trap
Weak Interaction Studies
Vud from mean Ft value
and muon decay
strength:
Vud2  Vus2  Vub2  0.9967  0.0014
Vud  0.9738  0.0004
 d w  Vud Vus Vub  d 
  
 
 sw   Vcd Vcs Vcb  s 
 b  V
 
 w   td Vts Vtb  b 
Q-Values needed for
superallowed 0+->0+ beta
emitters with A > 54
Combined with half-lives
and branching ratios this
will help extend the
number of well known Ft
values
e.g. 74Rb, t1/2 = 50 ms,
required δm/m = 1x10-8
current δm/m = 5x10-8.
ISAC
ion beam
RFQ
cooler &
buncher
EBIT
charge
breeder
m/q
selection
Penning
trap
Weak Interaction Studies
Vud from average Ft value 2
2
2
V

V

V
ud
us
ub  0.9967  0.0014
and muon decay
strength:
Vud  0.9738  0.0004
Q-Values needed for
superallowed 0+->0+ beta
emitters with A > 54
Combined with half-lives
and branching ratios this
will help extend the
number of well known Ft
values
e.g. 74Rb, t1/2 = 50 ms,
required δm/m = 1x10-8
current δm/m = 5x10-8.
ISAC
ion beam
RFQ
cooler &
buncher
EBIT
charge
breeder
m/q
selection
Atomic and Nuclear Mass Models
Penning
trap
ISAC
ion beam
RFQ
cooler &
buncher
EBIT
charge
breeder
Stellar Nucleosynthesis
Production of all the heavy
elements (A ≥ 7) take place via
nuclear reactions in the stars
In order to understand the
complex chains of nuclear
reactions that can take place
inside a star (e.g. the s-, p-, rand the rp- processes) it is
necessary to know the masses
of the nuclei involved
Such chains involve a large
number of short-lived nuclei
which lie close to the proton and
neutron drip lines
m/q
selection
Penning
trap
RFQ
cooler &
buncher
e--beam
EBIT
charge
breeder
B
m/q
selection
Penning
trap
axially:
electron
beam
space
charge
50
m
ISAC
ion beam
longitudinally:
electrodes
trap potential Ut  450 V
RFQ
cooler &
buncher
ISAC
ion beam
EBIT
charge
breeder
m/q
selection
Penning
trap
V
Ion Beam
EBIT cannot accept a continuous beam
Low emittance needed in order to traverse
magnetic field efficiently
Therefore, we need to cool and bunch the
ISAC beam
ISAC
ion beam
RFQ
cooler &
buncher
EBIT
charge
breeder
Standard quadrupolar
geometry focuses in one
direction and defocuses
in the other
( x2  y 2 )
 V
2
r0
2V
2V
E x   2 x, E y  2 y
r0
r0
m/q
selection
Penning
trap
ISAC
ion beam
RFQ
cooler &
buncher
EBIT
charge
breeder
m/q
selection
Penning
trap
However, it has long been known that by
placing a series of quadrupoles together
a net focusing force can be obtained
ISAC
ion beam
RFQ
cooler &
buncher
EBIT
charge
breeder
m/q
selection
Penning
trap
Alternatively, we can use RF- potential
to alternate the orientation of the
focusing and defocusing directions
ISAC
ion beam
RFQ
cooler &
buncher
EBIT
charge
breeder
m/q
selection
Penning
trap
By segmenting the structure we can also apply
a longitudinal field and hence create bunches
ISAC
ion beam
RFQ
cooler &
buncher
EBIT
charge
breeder
m/q
selection
Penning
trap
Thermalization of ion beam via interaction
with a buffer gas
Thermalization in three dimensions leads to
loss of beam
Counter longitudinal energy loss via the
application of an accelerating electric field
Ions disperse radially due to scattering of
forward momentum
Use RFQ ion trap to provide a force to
counteract the dispersion
Hence, a gas-filled RFQ can be used to cool
an ion beam
Sine-Wave Vs Square Wave:
What is required?
Sine-Wave q<0.908 Stable, q≈0.4 best.
4 zeV
q
,
2 2
m r0 Square-Wave q<0.712 Stable, q≈0.3 best.
The magnitude of V determines the depth of the
psuedopotential
This determines the traps acceptance, its transfer
efficiency and its space-charge limit. Thus, it is
desirable to have V as large as possible
If V is fixed ω must be able to vary in order to trap a
wide range of masses
7 ≤ m ≤ 235 u, 0.4 ≤ f ≤ 3 MHz @ 400 Vpp,
r0 = 10 mm
Experimental Viability:
Sine Wave
Inductor has limited bandwidth
Driving off resonance causes core to heat up
distorting induced wave
However, used in all other experimental
systems so the technology is proven
Experimental Viability:
Square-Wave
No lower limit on
frequency, upper
limit determined by
energy dissipation in
MOSFETs
Experimental Viability:
Square-Wave
Energy dissipation is determined by the
capacitance of the RFQ
Systems have previously been developed that
can run at up to Vpp = 1 kV at up to 1 Mhz
However, these have only been use to drive
3-d Paul traps or small quadrupole mass
filters, C ≈ 25 pF
The RFQ required for TITAN is significantly
larger than a 3-d trap and has capacitance on
the order of C ≈ 1500 pF
Square-Wave not possible with current
MOSFETs?
Experimental Viability:
Square-Wave
KICKER group at TRIUMF already had the
solution to the capacitance problem
By stacking MOSFETs it is possible to reduce
the energy dissipated by each chip
First system designed and tested Vpp = 400V,
f = 1 MHz (m ≥ 65)
Improvements underway to try and expand
to Vpp = 800 V, f = 3 MHz
Other benefits include: equations of motion
simpler than sinusoidal case, possibility to use
frequency scanning methods or varying duty
cycle to filter impurities
The Square-Wave Driver
The Square-Wave Driver
Properties of the RFQ from
Analytic Considerations
Meissner equations determine ions
motion in square-wave-driven trap:
t
2 x
2 y
.
 2qx  0,
 2qy  0,  
2
2


2
Analytic solution shows a simple
harmonic macro-motion perturbed by a
coherent micro-motion
As q increases so does the amplitude of
the micro-motion until at q = 0.712 the
motion becomes unbound
Properties of the RFQ from
Analytic Considerations
In Phase Space
Micro-motion distorts
ideal harmonic ellipse
Acceptance defined as
area of harmonic
ellipse whose
maximum distorted
amplitude = r0
Acceptance varies as a
function of q with a
maximum at q ≈ 0.3
q = 0.3
Temperature
Micro-motion is coherent and
therefore doesn’t contribute to the
temperature of the ions in the trap
Temperature of an ion cloud in a
harmonic potential can be defined
in terms of the standard deviation
in position and momentum space:
u 
1
s
kT
,  v  mkT .
m
Can use information from ellipses to
convert from σx and σv as a
function of phase/time to σx-SHM
and σv-SHM and hence define
temperature
Space-Charge Limit
Can use amplitude of harmonic
motion combined with secular
frequency to define the depth of
the psuedopotential
Use simple model for the beam
to get an idea of the space
charge limit
In continuous mode consider
beam to be an infinitely long
cylinder
In bunched mode consider
bunch to be a perfect sphere
m 2
E ps   s rmax
ze
For Cylinder:

I
Esc 
,
2 0 r
Vd
For Sphere:
Esc 
Q
4 0 R
2
Space Charge Limit
Continuous, Vd = 1000 m/s
Bunched, t = 1 ms
In continuous mode Imax ≈ 2 μA, @ q = 0.39
In bunched mode Imax ≈ 30 nA, @ q = 0.33
Modeling Buffer-gas Cooling:
Viscous Drag
Drift Velocity related to electric field by:
Vd  kE
Acceleration due to electric field countered by
deceleration due to scattering:
eE
eE
e Vd
aE 
, ad  

m
m
m k
Need mobility, k, as a function of drift velocity
At low energies (E < 10 eV) data exists, for
higher energies must extrapolate either using
tabulated values for (n,6,4) potentials or MC
simulation
Modeling Buffer-gas Cooling:
Viscous Drag
Cesium in helium
extrapolation by MC method
Cesium in nitrogen
extrapolation using tabulated values
250
k
m2s 1V
1
200
150
100
50
2000
4000
6000
Vd
8000
m s
10000
12000
Using this model we can calculate range and
cooling times
However, it tells us nothing of the final
properties of the cooled ions as all ions are
treated equally
14000
Modeling Buffer-gas Cooling:
Viscous Drag
v
v
m ini k (v)
m ini
dv
R   k (v)dv, tc 

e vtherm v
e 0
Cesium in 2.5x10-2 mbar Helium
Range fits with length of RFQ
predetermined to be 700 mm
Cooling times on order of 400 μs
fits well with 50 ms lifetimes
Range, etc., will vary depending
on weight of ion of interest
Can adjust range and cooling
time by varying pressure of the
buffer-gas, or using heavier gas
Modeling Buffer-gas Cooling:
Monte Carlo
Use ion-atom interaction potential to calculate
scattering angle in center of mass frame:


 cm    2b  1 

rm
b V (r ) 


2
r
Ecm 
2

1
2
dr
r2
Relate this to energy loss in lab frame:
mi2  mg2
2mi mg
Esc


cos( cm )
2
2
Ein (mi  mg ) (mi  mg )
Runs in SIMION or separately in C
Test by using to recreate experimental results
for the mobility of ions in the gas
Modeling Buffer-gas Cooling:
Monte Carlo
Lithium in helium perfect
agreement
Cesium in helium some
small discrepancies
Li+-He interaction
potential well known with
ab-initio calculations
possible
Cs+-He simple (8,6,4)
potential used. Much
disagreement about the
proper form in the
literature
Modeling Buffer-gas Cooling:
Monte Carlo
RFQ defined in SIMION r0
=10 mm, L = 700 mm,
Vpp = 400 V
Segmented into 24 pieces
with longitudinal potential
previously shown
Transfer of beam with
Cooling time approx. 2 x
98% efficiency
longer than that from drag
model
Modeling Buffer-gas Cooling:
Monte Carlo
Ions initialized in trap with
T = 800 K
Cooled for 500 μs and then
data recorded in 0.02 μs
intervals for 10 μs
Plot of temperature as a
function of q shows the
effects of RF-heating
Space-charge not yet
included so represents a
minimum possible
temperature
Test Setup
Injection Optics
Simulated 88% efficiency
limited by radius of
quadrupoles
Four-Way Switch
Use quadrupolar field to bend ions
through 90o
Switch polarity to bend in opposite
direction
Apply equal voltages to electrodes for undeflected path
Four-Way Switch
Minimum value for h = 0.4 r0
 x2  y 2 

  V 
2
 r0 
V independent of r0 but dependant on
h and ion energy
We took h = 0.15 r0
For ion energy = 30 keV, V =21.1 kV.
Strength of electric field determines
size of the steerer:
Emax
2V

r0
We took r0 = 17 mm, E ≈ 2.5 kV/mm
Extraction Optics
Extraction Methods
In absence of buffer-gas expect all bunches to have
the same longitudinal and transverse emittances
First extraction method releases ions with a small
energy spread and large time of flight spread
Second method reduces time of flight spread but
increases energy spread
Simulated Beam Properties
 rms  4
Buffer-gas heats beam so
emittances not constant
Kicking the ions hard out of
the trap reduces time of flight
spread and increases energy
spread
εrms = 3 p mm mrad @ 2.5
kV
x
2
.
.
x 2  xx
2
Experimental Setup
Experimental Setup
Experimental Setup: Injection
Experimental Setup: Injection
Beam through four-way
switch with approx. 75%
efficiency
Beam into RFQ with
approx. 25% efficiency
Currently trying to
diagnose source of loses
Beam charging isolators in
switch?
Experimental Setup: RFQ
Experimental Setup: RFQ
Installed and SquareWave successfully applied
to the rods
Beam passed through
RFQ and detected at the
RFQ exit
Experimental Setup:
Extraction
Experimental Setup:
Extraction
Extraction optics
installed
MOSFET switch
developed at McGill
used to switch RFQ dc
bias
Belhke 60 kV switch
used to pulse drift tube
Testing of drift tube
pulser underway
Summary and Outlook
Detailed simulations of cooling process in a squarewave driven RFQ carried out
Based on simulations system designed and built
Square-wave driver capable of driving large
capacitive loads at high voltage and high frequency
developed and tested
Testing of the system underway. Emittance rig is
being built so as to compare the actual beam
properties to simulation
TITAN platform now installed in proton hall
RFQ will be installed ready for the delivery of the
EBIT at the end of the summer
Thanks
Jens Dilling, Joe Vaz, Laura Blomeley and the rest of the
TITAN group.
Co-op Students: Robert Cussons, Ori Hadary, Amar
Kamdar, George Yuan.
Triumf Support: M. Good, H. Sprenger, M. McDonald, R.
Dube, R. Baartman, Controls Group, Design Office,
KICKER Group,
Machine Shop, Vacuum Group.