ESS#Linac#Simulator#vs.#TraceWineval.esss.lu.se/DocDB/0002/000254/001/Seminarino-ELSvsTW.pdf ·...
Transcript of ESS#Linac#Simulator#vs.#TraceWineval.esss.lu.se/DocDB/0002/000254/001/Seminarino-ELSvsTW.pdf ·...
ESS Linac Simulator vs. TraceWin
Emanuele LafacePhysicist
Accelerator Department
AD Seminarino
February 19th 2013
TDR 2012Power 5 MW
Peak Power 125 MWPeak Current 50 mAEnergy From 3 MeV to 2.5 GeV
Pulse Length 2.86 msDuty Cycle 4.00%Cavities 208Gradient 40 MV/mLength ~600 m
Simulated parameters for the ESS Proton Linac
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DRIFT 156.522 11 0
Available elements:Drift
2
6666664
1 L 0 0 0 00 1 0 0 0 00 0 1 L 0 00 0 0 1 0 00 0 0 0 1 L
�2�2
0 0 0 0 0 1
3
7777775
Tracewin input
Matrix
Available elements:Quadrupole
Tracewin input
Matrix
QUAD 22.5 -12.3918 12 0 0 0 0 0
2
6666664
cos(KL) sin(KL)K 0 0 0 0
�K sin(KL) cos(KL) 0 0 0 0
0 0 cosh(KL) sinh(KL)K 0 0
0 0 K sinh(KL) cosh(KL) 0 0
0 0 0 0 1
L�2�2
0 0 0 0 0 1
3
7777775
Available elements:Bending magnet
Tracewin input
Matrix
2
666666664
cos(Kx
L) sin(K
x
L)
K
x
0 0 0
1�cos(K
x
L)
⇢K
x
2
�Kx
sin(Kx
L) cos(Kx
L) 0 0 0
sin(K
x
L)
⇢K
x
0 0 cos(Ky
L) sin(K
y
L)
K
y
0 0
0 0 �Ky
sin(Ky
L) cos(Ky
L) 0 0
� sin(K
x
L)
⇢K
x
� 1�cos(K
x
L)
⇢K
x
L
2 0 0 1 �K
x
L�
2�sin(K
x
L)
⇢
2K
x
3 +
L
�
2
⇣1� 1
⇢
2K
x
2
⌘
0 0 0 0 0 1
3
777777775
BEND -11 9375.67 0 50 1
Available elements:Edge effect
Tracewin input
Matrix
EDGE -5.5 9375.67 50 0.45 2.8 50 1
2
66666664
1 0 0 0 0 0tan(�)|⇢| 1 0 0 0 0
0 0 1 0 0 0
0 0 � tan(�� )|⇢| 1 0 0
0 0 0 0 1 00 0 0 0 0 1
3
77777775
Available elements:DTL Cell
Tracewin input
Matrix
DTL_CEL 71.2854 22.5 22.5 0.00308396 0 -70.2647 156981 -34.6474 10 0 0.0838043 0.78447 -0.36933 -0.151042
2
6666664
1 L 0 0 0 00 1 0 0 0 00 0 1 L 0 00 0 0 1 0 00 0 0 0 1 L
�2�2
0 0 0 0 0 1
3
7777775
2
6666664
1 L 0 0 0 00 1 0 0 0 00 0 1 L 0 00 0 0 1 0 00 0 0 0 1 L
�2�2
0 0 0 0 0 1
3
7777775
2
66666664
k1C 0 0 0 0 0kxy
(��)o
k2C 0 0 0 0
0 0 k1C 0 0 0
0 0 kxy
(��)o
k2C 0 0
0 0 0 0 1 0
0 0 0 0 kz
(��)o
(��)i
(��)o
3
77777775
Drift Thin Gap Drift2
6666664
cos(KL) sin(KL)K 0 0 0 0
�K sin(KL) cos(KL) 0 0 0 0
0 0 cosh(KL) sinh(KL)K 0 0
0 0 K sinh(KL) cosh(KL) 0 0
0 0 0 0 1
L�2�2
0 0 0 0 0 1
3
7777775
2
6666664
cos(KL) sin(KL)K 0 0 0 0
�K sin(KL) cos(KL) 0 0 0 0
0 0 cosh(KL) sinh(KL)K 0 0
0 0 K sinh(KL) cosh(KL) 0 0
0 0 0 0 1
L�2�2
0 0 0 0 0 1
3
7777775
Quadrupole Quadrupole
Available elements:Cavity Multi gap
Tracewin input
Matrix
2
6666664
1 L 0 0 0 00 1 0 0 0 00 0 1 L 0 00 0 0 1 0 00 0 0 0 1 L
�2�2
0 0 0 0 0 1
3
7777775
2
6666664
1 L 0 0 0 00 1 0 0 0 00 0 1 L 0 00 0 0 1 0 00 0 0 0 1 L
�2�2
0 0 0 0 0 1
3
7777775
2
66666664
k1C 0 0 0 0 0kxy
(��)o
k2C 0 0 0 0
0 0 k1C 0 0 0
0 0 kxy
(��)o
k2C 0 0
0 0 0 0 1 0
0 0 0 0 kz
(��)o
(��)i
(��)o
3
77777775
Drift Thin Gap Drift
NCELLS 1 3 0.5 5.41203e+06 -50.6001 31 0 0.493611 0.488812 12.9855 -14.5316 0.400918 0.679564 0.395851 0.334978 0.657124 0.596556 0.26422 0.661268 0.590482 0.266148
2
6666664
1 L 0 0 0 00 1 0 0 0 00 0 1 L 0 00 0 0 1 0 00 0 0 0 1 L
�2�2
0 0 0 0 0 1
3
7777775
2
6666664
1 L 0 0 0 00 1 0 0 0 00 0 1 L 0 00 0 0 1 0 00 0 0 0 1 L
�2�2
0 0 0 0 0 1
3
7777775
2
66666664
k1C 0 0 0 0 0kxy
(��)o
k2C 0 0 0 0
0 0 k1C 0 0 0
0 0 kxy
(��)o
k2C 0 0
0 0 0 0 1 0
0 0 0 0 kz
(��)o
(��)i
(��)o
3
77777775
Drift Thin Gap Drift
...
Taking into account acceleration, time transit factor, etc.
Available elements:Space Charge
U
sc
(x, y, z) =eN
4p⇡
3✏0�
2
Z 1
0
e
� x
2
2�x
2+t
� y
2
2�y
2+t
� z
2
2�z
2+t � 1p(2�
x
2 + t)(2�y
2 + t)(2�z
2 + t)dt
F
x
=e
2N
2p⇡
3✏0�
2x
Z 1
0
e
� x
2
2�x
2+t
� y
2
2�y
2+t
� z
2
2�z
2+t
p(2�
x
2 + t)3(2�y
2 + t)(2�z
2 + t)dt
F
y
=e
2N
2p⇡
3✏0�
2y
Z 1
0
e
� x
2
2�x
2+t
� y
2
2�y
2+t
� z
2
2�z
2+t
p(2�
x
2 + t)(2�y
2 + t)3(2�z
2 + t)dt
F
z
=e
2N
2p⇡
3✏0�
2z
Z 1
0
e
� x
2
2�x
2+t
� y
2
2�y
2+t
� z
2
2�z
2+t
p(2�
x
2 + t)(2�y
2 + t)(2�z
2 + t)3dt
Available elements:Space Charge
U
sc
(x, y, z) =eN
4p⇡
3✏0�
2
Z 1
0
e
� x
2
2�x
2+t
� y
2
2�y
2+t
� z
2
2�z
2+t � 1p(2�
x
2 + t)(2�y
2 + t)(2�z
2 + t)dt
F
x
=e
2N
2p⇡
3✏0�
2x
Z 1
0
e
� x
2
2�x
2+t
� y
2
2�y
2+t
� z
2
2�z
2+t
p(2�
x
2 + t)3(2�y
2 + t)(2�z
2 + t)dt
F
y
=e
2N
2p⇡
3✏0�
2y
Z 1
0
e
� x
2
2�x
2+t
� y
2
2�y
2+t
� z
2
2�z
2+t
p(2�
x
2 + t)(2�y
2 + t)3(2�z
2 + t)dt
F
z
=e
2N
2p⇡
3✏0�
2z
Z 1
0
e
� x
2
2�x
2+t
� y
2
2�y
2+t
� z
2
2�z
2+t
p(2�
x
2 + t)(2�y
2 + t)(2�z
2 + t)3dt
The three forces must be applied in the framework of the bunch, so they are not the same because z -‐> γz
Available elements:Space Charge
U
sc
(x, y, z) =eN
4p⇡
3✏0�
2
Z 1
0
e
� x
2
2�x
2+t
� y
2
2�y
2+t
� z
2
2�z
2+t � 1p(2�
x
2 + t)(2�y
2 + t)(2�z
2 + t)dt
This integral cannot be expressed in terms of elementary functions.
Z 1
0
e� x
2
2�x
2+t
� y
2
2�y
2+t
� z
2
2�z
2+t
p(2�
x
2 + t)3(2�y
2 + t)(2�z
2 + t)dt
Common strategies adopted to solve it:
Z 1
0
e� x
2
2�x
2+t
� y
2
2�y
2+t
� z
2
2�z
2+t
p(2�
x
2 + t)3(2�y
2 + t)(2�z
2 + t)dt
-‐ Linear approximation and long bunch: x ! 0, y ! 0,�z
� �
x
,�
y
K.Y. Ng, “The transverse Space-Charge force in tri-gaussian distribution”, Fermilab-TM-2331-AD, 2007.
10
Common strategies adopted to solve it:
Z 1
0
e� x
2
2�x
2+t
� y
2
2�y
2+t
� z
2
2�z
2+t
p(2�
x
2 + t)3(2�y
2 + t)(2�z
2 + t)dt
-‐ Linear approximation and long bunch: x ! 0, y ! 0,�z
� �
x
,�
y
K.Y. Ng, “The transverse Space-Charge force in tri-gaussian distribution”, Fermilab-TM-2331-AD, 2007.
-‐ Elliptical uniform bunch:
P.M. Lapostolle, “Effets de la charge d’espace dans un accelerateur lineaire a protons”, CERN AR/Int. SG/65-15, 15 Juillet 1965.
U
sc
(x, y, z) = V0 �⌧
2✏0
"x
2+ y
2
2
+ a
2 z �x
2+y
2
2
b
2 � a
2
1�
acosh(
ba )bp
b
2 � a
2
!#.
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Common strategies adopted to solve it:
Z 1
0
e� x
2
2�x
2+t
� y
2
2�y
2+t
� z
2
2�z
2+t
p(2�
x
2 + t)3(2�y
2 + t)(2�z
2 + t)dt
-‐ Linear approximation and long bunch: x ! 0, y ! 0,�z
� �
x
,�
y
K.Y. Ng, “The transverse Space-Charge force in tri-gaussian distribution”, Fermilab-TM-2331-AD, 2007.
P.M. Lapostolle, “Effets de la charge d’espace dans un accelerateur lineaire a protons”, CERN AR/Int. SG/65-15, 15 Juillet 1965.
U
sc
(x, y, z) = V0 �⌧
2✏0
"x
2+ y
2
2
+ a
2 z �x
2+y
2
2
b
2 � a
2
1�
acosh(
ba )bp
b
2 � a
2
!#.
-‐ Numerical integration: I adopted this solution using an adaptive algorithm for the Gaussian quadrature.R. Pissens et al., “QUADPACK, A Subroutine Package for Automatic Integration”, Berlin : Springer, 1983.
P. Gonnet, “Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants”, ACM Trans. on Math. Soft. Vol. 33, Issue 3, Article 26 (2010).
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Common strategies adopted to solve it:
-‐ Elliptical uniform bunch:
Some results
DTL to Target October 2012 Lattice
I=0, No Space Charge, Horizontal plane12
Some results
DTL to Target October 2012 Lattice
I=0, No Space Charge, Vertical plane13
Some results
DTL to Target October 2012 Lattice
I=0, No Space Charge, Longitudinal plane14
Some results
DTL to Target October 2012 Lattice
I=50 mA, Horizontal plane15
Some results
DTL to Target October 2012 Lattice
I=50 mA, Vertical plane16
Some results
DTL to Target October 2012 Lattice
I=50 mA, Longitudinal plane17
Some results
DTL to Target October 2012 Lattice
I=50 mA, 10 σ, Horizontal plane with machine aperture18
Some results
DTL to Target October 2012 Lattice
I=50 mA, 10 σ, Vertical plane with machine aperture19
Future developments
XML input and output functionality.
Matching module for the initial conditions.
Multi-‐particles version.
Better model for RF cavities: analytical `ield solver or `ield map.
User Interface.
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