P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 1
Heavy-Ion Beam Dynamics in the RIA Acceleratorsand Development of RT Accelerating Structures for the RIA
• Layout of the RIA accelerators.• Acceleration of multiple-charge state heavy-ion beams.• Driver Linac:
- Injector system: ECR-LEBT-RFQ;- Design of 57.5 MHz cw RFQ;- Parametric resonance of transverse motion;- Beam steering compensation and electric field
symmetry in SRF cavities;- Beam Dynamics optimization and simulation;- Isopath transport of multi-q beams;- BD in high-E section: Triple-Spoke vs Elliptical cavities.
• Design of the Post-Accelerator:- RT accelerating structures and beam dynamics.
• Summary and outlook.
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 2
Rare Isotope Accelerator Facility
4007373He
100 (400)400238U
400451136Xe
400900p
Beam power (kW)
Beam energy (MeV/u)
Species
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 3
Beam
Beam
f, MHz 57.5 57.5 57.5 115 172.5 345
f, MHz 805 805 805
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 4
ANL spoke cavity
JLABellipticalcavity
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 5
Acceleration of synchronous particle
sc0us TLeEA
qW M' cos,
Aq
constEconstE
A
q00 /
,
0n
qsnsn0n
EA
qconst
constEA
qn ,cos,cos MM
0s0
snn
A
q
A
q,coscos MM
Fixed velocity profile(RFQ, RT DTL)
Multi-q heavy-ionaccelerator
Variable velocity profile(SC Linac)
E0=const,Tune phases of individual cavities
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 6
-60
-50
-40
-30
-20
-10
0
65 70 75 80 85 90
Charge state
Pha
se (
deg)
Synchronous phase as a function of uranium ion charge state. The designed synchronous phase is
–30q for q0=75.
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 7
E0
q=75
Ms
Eg(z)
-0.15 -0.1 -0.05 0 0.05 0.1 0.15
Distance, m
Zt
q=77
q=73
Earlier arrival Later arrival
Single accelerating gap
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 8
' p /p , % 2 q = 7 7 q = 7 5 1 q = 7 3 0 -1 -2 -8 0 -4 0 0 4 0
P hase , d e g
-0.8
-0.4
0
0.4
0.8
-15 -10 -5 0 5 10 15
Phase (deg)
'p
/p (
%)
q=77 q=75 q=73
Separatrix and small longitudinal oscillations
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 9
xxxx
xxxxx
xxxxx
xxxx
M
HEDJ
PDPPJ
PEPDP
c�c�
»¼
º«¬
ª��
�
22 2
sincossin
sinsincos
Lf
SRF cavitiesSolenoid
Transverse beam dynamics
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 10
54
56
58
60
62
64
72 73 74 75 76 77 78
Charge state
Pha
se a
dvan
ce
Px
(deg
)
0
100
200
300
400
500
Pha
se a
dvan
ce
)x
(deg
)
Px
)x
Phase advance over the period Px and total phase advance )x (modulo 360 q) in the medium-beta
section (12 MeV/u – 85 MeV/u)
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 11
0
10
20
30
40
1 2 3 4 5 6 7 8 9 10
Emittance growth factor
N/N
0, %
Transverse emittance growth in the focussing channel with alignment errors (±300 Pm)
Corrective one-element steering
No steering
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 12
Stripping foil
ECR ion source
Booster Injector
ATLAS section
Diagnostic area
40q Bend Reg ion
Slits, Faraday Cup
Multi-q beam experiment on ATLAS (ANL)
W=1.2 MeV/uq=35,36,37,38,39,40,41,42,43,44
W=2.9 MeV/u
q_average=51
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 13
-3
-2
-1
0
1
2
3
-30 -20 -10 0 10 20 30
Phase, deg
'W
/W, %
35+
36+
37+
38+
39+
40+
41+
42+
43+
Beam Dynamics Simulations
0
0.25
0.5
0.75
1
1.25
0 400 800 1200 1600
Distance, cmB
ea
m s
ize
, cm
35+ 36+37+ 38+39+ 40+41+ 42+43+
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 14
35 36 37 38 39 40 41680
690
700
710
Measurement
Simulation
Bea
m E
nerg
y (M
eV)
Charge State
Multi-q beam energy at the exit of the Booster
Equivalent to the RIA design req.
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 15
0.00
0.05
0.10
0.15
0.20
0.25
35 36 37 38 39 40 41 42 43 44
Charge state
Nor
mal
ized
cur
rent
(re
l. va
lue)
94% Transmission of Multi-Q Accelerated Beam Through the Booster
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 16
Accelerating and Focusing Lattice of the Driver Linac
Focusing:• In the DTL: superconducting solenoids.• In the high-E linac: warm SNS-type quadrupole
doublets (baseline design) or SC solenoids.• Length of focusing period is determined by the
stability conditions and required small beam size for high-intensity ion linacs:
- DTL: Raperture/R rms_beam= 11-12- High-E linac: Raperture/R rms_beam= 20-25
Acceleration:
• Superconducting resonators except in the Front End.
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 17
Layout of the Driver Linac
Front End
RFQ LEBTMEBT
Low-E
High-E
Medium-E
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 18
Low-energy achromatic 120° bend
Phase space plots
-10 -8 -6 -4 -2 0 2 4 6 8 10
-30
-20
-10
0
10
20
30
Ex=E
y =100p mm*mrad
y plane
x (bending) planex|,y| mrad
x,y mm
B
-6 -4 -2 0 2 4 6
-40
-30
-20
-10
0
10
20
30
Q=29
Q=28
Ex=124pmm*mrad x
| ,mrad
X ,mm
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
-15
-10
-5
0
5
10
15
Q=29
Q=28
Ey=132 pmm*mrad
y| ,mrad
y ,mm
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 19
Longitudinal phase space plots of two-charge state uranium beam along the LEBT
21
20
q1
q1
1
cAm
eV22
L�
O
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 20
�CW regime;
� Wide dynamic range of rf power level from P0/70 to P0for acceleration of various ion species from protons to uranium;
� Simultaneous acceleration of two charge-state heavy-ion beams;
� Maintaining an extremely small longitudinal emittance formed by the external multi-harmonic buncher;
� Exit of the RFQ: beam waist in both H- and V-planes for easer matching to the following MEBT.
Basic features of the 57.5 MHz RFQ
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 21
• Adiabatic bunching;• Internal ‘klystron’ bunching;• External multi-harmonic buncher: Extremely low long.
emittance (ISAC-1 RFQ, TRIUMF). Simultaneous acceleration of 2 charge states for heavy ions.
RFQ design options
a) High-efficiency SRF cavities for the following acceleration;
b) Moderate peak surface fields in the RFQ to provide reliable operation in CW mode;
c) High quality two-charge-state beam parameters;d) Large transverse acceptance.e) Possibility to increase inter-vane voltage to accept lower
charge states (higher intensities!).
Frequency is 57.5 MHz:
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 22
Accelerating by an RFQ
2
1
2
2
0
EO
EO
S
�
cL
m
aR
k
ma
a - Aperture
- Maximum distance from axis to electrodes
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 23
RFQ resonant structure
~4000
I 510
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 24
Vane Tip
¸¹
ᬩ
§��
�
¸¹
ᬩ
§��
�
kzsin1m
1m1Ry
kzsin1m
1m1Rx
0
0
eR2
Longitudinal modulationTransverse cross-section
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 25
-2 -1 0 1 20
1
2
3
4
5
6
Ele
ctric
fie
ld (
MV
/m)
Distance from RFQ center (m)
-2 -1 0 1 2-8
-6
-4
-2
0
2
4
6
8
Ele
ctric
fie
ld (
MV
/m)
Distance from RFQ center (m)
Electric field distribution along the RFQ
f=57.5 MHz
Absolute
Ex Ey
Operating mode f=57.5 MHz
Upper mode 1 f=68.4 MHz
f=93.5 MHz
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 26
Cross Section of the Octagonal ResonatorS
= 5
13
S = 513
Internal dimension
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 27
� �����
����> @
������
�����> @
�����
����> @
�����
����> @
57.5 MHz RadioFrequency QuadrupoleAccelerator
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 28
RF Induced Heat Flux
Heat FluxW/cm2
Heat flux distribution determined with ANSYS RF analysis, heat loads scaled to 8.0 kW per segment
0.0 1.84 2.76 3.68 4.60 5.52 6.44 7.36 8.28.92
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 29
Radial displacements of Vanes at symmetry plane
Radial Displacementinches
-1.94e-3 inches
-2.58e-4
-1.91e-3
-2.59e-4
-1.94e-3 -1.73e-3 -1.51e-3 -1.30e-3 -1.08e-3 -8.62e-4 -6.46e-4 -4.29e-4 -2.14e-4 2.30e-6
Path 1this vane at tipstart this sidesee next slide
Path 2this vane at tipstart this sidesee next slide
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 30
Characteristics of the RFQ resonator
• Modular structure. The brazing technique which is well established for 4-vane RFQs can be applied. Brazing provides the best electrical properties of rf structures;
• Small transverse dimensions for low frequencies;• Large frequency separation of non-operating modes;• Uniform field distribution along the z-axis;• High shunt impedance (45 kW for 4 meter structure);• Symmetric design guarantees low field perturbations
due to possible thermal distortion, no dipole component of the fields in the aperture;
• Provides good mechanical stability of the construction together with precise alignment ability.
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 31
¦
¦
¦
¦ ¦
f
��
f
��
f
�
�
f
f
�
���
���
��¸̧¹
·¨̈©
§
»¼
º«¬
ª�����
042,1212
0)12(212,22
0
)12(2
012,00
1 112202
4cos])12[(),(
)12(2cos)2(),(
)12(2cos),(
)12cos(),(2cos),(),(),,(
mmmnn
mmmnn
m
m
m
n nnn
U
mkrnIArF
mnkrIArF
mR
rArF
kznrFnkzrFrFzrU l
-T
TT
TT
T-T-
104
AT �
S
- Accelerating efficiency
01
2
02
0
2
4A
Rcm
UeK l
¸¸¹
·¨¨©
§�
O- Focusing efficiency
Electric potential in RFQ aperture
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 32
Coupling of Longitudinal and Transverse Motions
Separatrix of longitudinal oscillationscalculated at the beginning of the RFQ(k=2.38)
� �� �)sin(Icos2
),H( 00
02
ss zkkrzkAW
TZeUcz MM
S
EE �'�'�
' ''
-8 -4 0 4
-0.2
-0.1
0.0
0.1
'E 1
03
'z (mm)
R=0.4 mm
R=0.25 mm
R=0
Initial particle distribution
sEEE � ' Difference between particle velocity and synchronous value
czzz � ' The corresponding difference between longitudinal coordinates
EO
S2 k
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 33
Longitudinal emittances at the exit of RFQ
Phase (deg) Phase (deg)
Phase (deg) Phase (deg)
'W
/W (
%)
'W
/W (
%)
'W
/W (
%)
'W
/W (
%)
1 2
3 4
0.5 1.0 1.5
1.4
1.6
1.8
2.0
2.2
2.4
2.6
Norm. transverse emittance (S mm mrad)
Out
put l
ong.
em
ittan
ce
( S k
eV/u
nse
c)1
2
3
4
Longitudinal emittance99.9 % of particles
50000 particles are simulated
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 34
Transverse Emittances at the RFQ Exit
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4
-0.01
0.00
0.01
0.02
dX/d
z (m
rad)
X (cm)-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
-0.01
0.00
0.01
0.02
dY/d
Z (
mra
d)Y (cm)
X plane Y plane
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4
-0.01
0.00
0.01
0.02
dX/d
z (m
rad)
X (cm)-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
-0.01
0.00
0.01
0.02
dY/d
Z (
mra
d)Y (cm)
X plane Y plane
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 35
BEAM RESONATOR TYPE 2-GAP QWR, EG=0.062, f=57.5 MHz 2-GAP QWR, EG =0.15, f=115 MHz
BEAM
BEAM
RESONATOR TYPE
2-GAP HW, EG=0.19,f=172.5 MHz
4-GAP SPOKE, EG =0.5,f=345 MHz
BEAM
BEAM
3.98 m
BEAM
5.80 m
4-GAP SPOKE, EG =0.5, 0.62f=345 MHz
RIA Driver Linac
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 36
Driver Linac
400-580177-250113-177Length of the focusing period, cm
46 (38)2010Number of cryostats
805 (345)172.5-34557.5-115Frequency, MHz
105
52
129
20
10.1-85.0
Medium E
28.520Surface field SRF cavities, MV/m
260 (197)55Length, m
46 (38)42Number of focusing periods
166 (140)85Number of resonators
81.0-403.00.2-10.2Uranium beam energy, MeV/u
High ELow E
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 37
Some design solutions � Multi-q beam acceleration.� Low longitudinal emittance of two charge-state uranium beam.� Inter-cryostat space will contain only vacuum valves and a small beam
diagnostics box. � Beam steering coils will be combined with the SC focusing solenoids
and will not require an additional space along the beamline.� Standard accelerating SRF cavities can be switched to the mode of a
beam phase monitor in order to set up phases and amplitudes of the accelerating fields in the upstream cavities.
� Transverse matching between the cryostats is facilitated by the absence of the first SRF cavity in the very first focusing period of the cryostats.
� Long. matching between the cryostats is provided by the setting of phases in the SRF cavities.
� Beam energy at stripper locations is determined from the condition of lowest possible long. emittance of multi-q uranium beam.
� Triple spoke cavities vs elliptical.
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 38
Simulation codes • TRACE, TRANSPORT, COSY, GIOS;
• CST Microwave Studio; SIMION;
• DESRFQ, DYNAMION;
• RAYTRACE, TRACK.
TRACK:
• multiparticle simulation of multi-q ion beams in 6D phase space;
• 3D electromagnetic fields from MWS in rectangular mesh;• Fringing fields of magnets and multipoles as in RAYTRACE code;
• Realistic fields in solenoids;
• Integration of equations of motion by 4th order Runge-Kutta method;
• Misalignments and random errors are included.
Detailed BD simulations are necessary for cost-effective design of the accelerators
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 39
Beam envelopes along the driver linac
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 40
The condition for a n-th orderparametric resonances of transverse motion in a smooth approximation lt 2
nPP
Resonance width sn2tsn ba 'P' ��
� � 2u
sm2f
3ss
scm
sineES1
A
q
2
M
OJE
S' Defocusing factor
sl 2 'P
n=1 and Ms=30q: a1| 0, b1|1.79n=2 a2| 3.93, b2|4.31.
Longitudinal phase advance
Parametric resonance
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 41
0 100 200 300 400
20
40
60
80
100
n=2
n=1
Pha
se a
dva
nce
(de
g)
Beam Energy (MeV/u)
EG=0.49
EG=0.62
EG=0.81
0 100 200 300 400
20
40
60
80
100
n=2
n=1
Pha
se a
dva
nce
(de
g)
Beam Energy (MeV/u)
EG=0.49
EG=0.62
EG=0.81
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 42
0
1
2
3
4
0 10 20 30 40 50 60 70
Distance (m)E
mitt
ance
gro
wth
fact
or
Hz
Hx
Hy
RMS emittance, Pt=30q
Emittance containing99.9% of the particles
DTL section, 172. 5 MHz
0
1
2
3
4
0 10 20 30 40 50 60 70
Distance (m)
Em
ittan
ce g
row
th fa
ctor
Pt =30°
Pt =50°Pt =40°
Win=10 MeV/u
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 43
Emittance evolution along the ECL linac for 4-cavity and 3-cavity lattices
1
1.1
1.2
1.3
0 10 20 30 40 50 60 70 80 90
Distance (m)
Em
ittan
ce g
row
th fa
ctor
3-cavity
4-cavity
$90 tP
Emittance evolution along the ECL linac for 4-cavity and 3-cavity lattices
1
1.1
1.2
1.3
0 10 20 30 40 50 60 70 80 90
Distance (m)
Em
ittan
ce g
row
th fa
ctor
3-cavity
4-cavity
$90 tP
BEAMBEAMProposed latticefor the first sectionof the ECL (EG=0.49)
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 44
0 5 10 15 20 25 30 35 40-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
Hx
Ez
10*Ey
Distance (cm)
10*E
y, Ez (
MV
/m)
-8
-6
-4
-2
0
2
4
6
8
Hx (
kA/m
)
Beam steering in QWR*
*A. Facco&V. Zviagintsev PAC91, N. Kakutani et al in EPAC98
Beam
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 45
D727 D(G�D(I�D+
dz)kzsin()z(E-C2/L
2/Lyd0Ed ³ �
�
MD
dz)kzsin(z
)z(E
2
Cy 2/L
2/L
z00Ef ³ �
w
w
�
MD
dz)kzcos()z(HCc2/L
2/Lx00H ³ �
�
MPED
Beam center deflection angles in QWR
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 46
0 5 10 15 20 25 30 35 40-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
Hx
Ey
Ez
D istance (cm )
Ey,
Ez (
MV
/m)
-8
-6
-4
-2
0
2
4
6
8H
x (kA
/m)
Compensation of the beam-steering effect(1) By cavity displacement in vertical plane: useful for heavy ions,
accepted as a baseline design for the ISAC-II(2) By reshaping of the drift tubes: universal far all regimes.
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 47
-1.2
-0.8
-0.4
0
0.4
0.05 0.15 0.25 0.35
E
Def
lect
ion
angl
e (m
rad)
Without compensation
With compensation
Beam steering in QWR
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 48
Defocusing asymmetry in 106 MHz QW SRF resonator, EEG=0.085, q/A=1
-0.5
0
0.5
1
1.5
2
2.5
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
beta
Def
ocus
ing
angl
e (m
rad)
x=1mm
(-y-0+y2_)/2
Defocusing field asymmetry in DT SRF cavities*
*Details will be presented in EPAC2002 by B. Laxdal, P.N. Ostroumov and M. Pasini.
Beam
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 49
Defocusing angles in 57.5 MHz QW SRF resonator, EEG=0.062, q/A=1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
beta
Def
ocus
ing
angl
e (m
rad)
x=1mm
(y1_75mm-y-0_25mm)/2
Defocusing field symmetry in DT SRF cavities
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 50
QUADRUPOLE COMPONENT OF TRANSVERSERF ELECTRIC FIELD
0 5 10 15 20 25
-50000
0
50000
EI
quad
Er
quad
Er
axial
Er,E
I , V/cm r=2/3R
a
z ,cm
Harmonic analysis of the electric field along the axis of HWR in cylindrical coordinates
)2sin(21
)2cos(22
)2cos(
22
2020
222
220
I
I
I
I rAr
V
rE
rArAr
VE
rArAV
r
� w
w�
� w
w�
��
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 51
Longitudinal phase space, W=199 keV/u
Input beam, 2 charge states:100% of particles2.4 S keV/u-nsec0.5 S mm-mrad
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 52
0
0.25
0.5
0.75
1
1.25
1.5
0 10 20 30 40 50 60Distance (m)
Bea
m s
ize
(cm
)
Yrms
Ymax
Yerror
Cavity aperture
Beam envelopes along the prestripper section
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 53
0
5
10
15
20
1 1.2 1.4 1.6 1.8 2 2.2 2.4
Emittance growth factor
N/N
0 (%
)
RMS emittance growth of two-charge state uranium beam in themisaligned focusing channel of low-E linac with the steering correction.
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 54
Compact 9 Tesla SC Magnet Assembly
-2
0
2
4
6
8
10
-30 -20 -10 0 10 20 30
Distance (cm)
Mag
netic
Fie
ld (
T)
Higher current in the bucking coils
Lower current in the bucking coils
Focusing by SC solenoids:- proven technology with SC resonators; - multi-q beam is less sensitive to mismatched conditions;- the fringing fields can be suppressed by bucking coils;- alignment of the solenoids should be easier;- beam is less sensitive to solenoid misalignments.
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 55
1
2
3
4
5
0 10 20 30 40 50 60
Distance (m)
Long
itudi
nal r
ms
emitt
ance
(4S
keV
/u-n
sec)
q=28.5
q=28 and 29
Longitudinal emittance along the prestripper linac
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 56
-2.00E-04
0.00E+00
2.00E-04
-1.20E-01 0.00E+00 1.20E-01
phase (rad)
' 'W
/W (
%)
q=69 q=73
Particle trajectories in the longitudinal phase space
Synchronous phase
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 57
Longitudinal phase space, W=9.4 MeV/u
10 S keV/u-nsec
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 58
29 S keV/u-nsec
Phase space plots of 5 charge state uranium beam at the location of second stripper linac
85 MeV/u
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 59
-20 -10 0 10 20-0.50
-0.25
0.00
0.25
0.50
Ene
rgy
Spr
ead
(%)
Phase (deg of 805 MHz)
Phase space plots of four charge state uranium beam at the exit of the driver linac. Includes all rf field errors and multiplicity
of charge states throughout whole SC Linac
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 60
-1 0 1 2 3 4 5 6 7 8-1
0
1
2
3
4
5
6
7
8
Dis
tanc
e (m
)
Distance (m)
Q1,2
SRF
B8
B7
B6
B5B
4B3
B2
B1
Q8Q
3
Q9,10
Q6,7
Q4,5
0 2 4 6 8 10 12 14 16 18
-40
-30
-20
-10
0
10
20
30
40
q=90q=88-92
B7,8
B5,6SRFB
3,4B
1,2
Q9,10
Q8
Q6,7
Q4,5
Q3
Q1,2
y (mm)
x (mm)
s (m)
System for selecting multiple q state beams through a 180° bend at 80 MeV/u.
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 61
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6-5-4-3-2-10123456 q=91
q=90 q=89
l (mm)
GK (x10-3)
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3 q=91 q=90 q=89
y (mm)
b (mrad)
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3 q=91 q=90 q=89
x (mm)
a (mrad)
-15 -10 -5 0 5 10 150
2
4
88899091Z=92
x ,mm
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 62
Main sources of longitudinal emittance growth:- Multiplicity of charge state (different synchronous
phase, frequency jumps);- Random errors of rf field;- Passage through the stripper;- Coupling of r-z motion in the RFQ.
Main sources of transverse emittance growth:
- Coherent oscillations of multi-q beams due to the misalignment of focusing elements;
- Mismatch of multi-q beam;- Passage through the stripper;- Higher-order distortions in the post-stripper transport
systems.
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 63
RMS emittance growth of multi-q uranium beamin the driver Linac
1.831.05High-E
12.34.4TOTAL
1.041.12Stripper 2
5.241.95Medium-E
1.11.06Stripper 1
1.121.80Low-E
LongitudinalTransverse
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 64
Triple Spoke vs Elliptical
MS=-30o MS=-25o
BEAM
3.98 m
BEAM
5.80 m
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 65
Triple Spoke vs Elliptical
ECL TSCL Number of cavity types 3 2 Peak surface field (MV/m) 27.5 28. Frequency (MHz) 805 345 Total number of cavities 188 140 Number of cryostats (focusing periods) 47 38 Length in the tunnel (m) 260 200 Operating temperature (qK) 2.1 4.5 Synchronous phase (deg) -30 -25 Longitudinal acceptance (keV/u-nsec) 60 280 Aperture diameter (mm) 80 40 Transverse normalized acceptance (S mm-mrad) 70 35
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 66
0
0.4
0.8
1.2
1.6
2
0 50 100 150 200
Distance (m)
Bea
m s
ize
(cm
)
rms size
Maximum size
Cavity aperture
0
5
10
15
20
25
0 50 100 150 200
Distance (m)
Pha
se (
deg)
rms width
(full width)/2
Synchronous phase
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 67
12
11
10
5 9
1 2 3 4 6 7 8
6.9 –20 MeV/u
0.68 –2.0 MeV/u
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$FFHOHUDWLQJ�VWUXFWXUHIRU�WKH�+\EULG�5)4�I �������0+]
���8��
9 ����N93FDOFXODWHG ���N:/ ����P:LQM ���NH9�X:H[LW ���NH9�X
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 69
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 70
Particletrajectories in the Hybrid RFQ
P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 71
Summary
• The technique of multi-q beam acceleration and transport is understood well;
• A detailed design has been developed for the focusing-accelerating lattice of the RIA accelerators;
• Substantial progress has been made in beam dynamics studies in the SRF DTL;
• Detailed BD studies in the driver linac taking into account errors and misalignments have been carried out;
• Several design concepts related to the driver linac have been successfully tested on the existing SC linac ATLAS.