Fast orbit bump magnet Use of magnetic field varying with time Multi-turn septum injection Orbit...
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Transcript of Fast orbit bump magnet Use of magnetic field varying with time Multi-turn septum injection Orbit...
Fast orbit bump magnet
• Use of magnetic field varying with time Multi-turn septum injection Orbit shift for phase-space painting of H- injection
• Use of pulse magnetic field at the peak value Orbit shift close to the septum magnet for a fast extraction
• Use of pulse magnetic field at flat-top Chicane bump for H- injection Orbit shift close to the septum magnet for a slow extraction
1
Orbit shift multi-turn injection by septum magnet
Fig. 1 The principle of the multi turn injection
Use of decay field by critical damping
The principle of the power supply circuit and its waveform are shown in Fig.2The critical damping of the circuit is given as,The excitation current is given by next equation,
CLR 4
L
Rt
L
CVi exp0
Fast decay
Slow decay
Fig.2 Principle of the circuit
Fig.3 Actual power supply circuit 1μs/div, 2V/div (50A/V)
1μs/div, 2V/div (50A/V)
Half sine wave by LC circuit for the use of peak value. Short time orbit-shift within the td
Half sine
Voltage recoverVoltage recover
Combination of LC resonant circuit and LR damping circuit
5μs/div, 5V/div (1kA/V) 2μs/div, 5V/div (1kA/V)
Principle of the circuitActual power supply circuit
5μs/div, 5V/div (1kA/V) 5μs/div, 5V/div (1kA/V)
Fast orbit bump magnet for orbit shift multi-turn injection
• Fast decay time (3~6 μs) • Ferrite is used for the core material.• Swing of the magnetic field is not allowed (for injection)
Temperature characteristicsFrequency characteristics
Characteristics of Ferrite (Fe2O3)
Longitudinal field distribution (measured value)
Excitation characteristics
Caution ! For “window frame” and “H-type core”
• Shorted-magnetic circuit enclose the beam.• Magnetic resistance is very low.• Strong magnetic field is induced around bunched beams.
• Open-magnetic circuit• Magnetic resistance is high.• Magnetic field induced around bunched beams is low.
C-type is better !
Orbit bump magnet for Charge exchange injection
Stripping Foil
Charge-exchange injection by chicane bump magnets
Parameters of H- injection bump magnet for the KEK Booster
Cross section of the core with “end–slit”
Properties of core material (0.1 mm Thick silicon steel, Nihon Kinzoku ST-100)
B-H characteristics Iron loss
Excitation characteristics of the magnet
Longitudinal field distribution of chicane bump magnets
Longitudinal field distribution of single bump magnet
Waveform of injection bump magnets(Use of magnetic field at the flat-top)
20μs/div, 2V/div, (1kA/V)
Pulse power supply by a pulse-forming-network (PFN)
Rising phase of the wave form Falling phase of the wave form
Ladder-typeLine-type
Ladder-type
tL
z
z
Vi 0
0
exp1
dttL
z
z
Vi 0
0
exp
Pulse forming network for chicane bump magnets (Using flattop field for injection)
PFN voltage, Magnet current and Magnet voltage
50μs/div, 2V/div (1kA/V)
1ms/div, 5V/div (1kV/V)
50μs/div, 0.5V/div
Let’s consider the part of transmission line as,
Fundamentals of Transmission Line Theory“Exact transitional solution”
On the one side line, partial resistance and inductance per unit length are (R/2) and (L/2) respectively. By the go and the return the values become R and L. The capacitance and conductance between two lines are defined as C and G respectively.
x x + Δx
dt
xdixLxRxixxvxv
)()()()(
dt
xdvxCxGxvxxixi
)()()()(
Equations for v and i are given as,finite difference equation.
Divide both sides by Δx and in the limit of Δx→0, we can get next differential equations.
dt
txiLtxRi
x
txv ),(),(
),(
t
txvCtxGv
x
txi
),(),(
),(
These simultaneous partial differential equations are known as “Telegraphy equation”
(1)
(2)
t
vC
x
i
t
iL
x
v
=-
=-∂
2
2
22
2
2
2
22
2
∂
∂1
1
t
i
cx
i
t
v
cx
v
=
=
)()( 21 ctxvctxvv -
)}+(+)({= 21 ctxvctxvLCi -
In the case of lossless transmission line, i.e. R = G = 0.The telegraphy equation becomes
),( txvv ),( txii
We can get wave equations. Here LC
c 1
(3)
(4)
The solution of Eq.(4) is given as,
v and i must satisfy the Eq.(3), we can get next solution for i,
(5)
(6)
Here,
)0,(
)0,(
xCvsCVdx
dI
xLisLIdx
dV
--
--
Eq.(5) and (6) satisfies wave equation. Final solution can be obtained by initial condition of “t” and boundary condition of “x”. Here we define the initial value of “v” and “t“ as v(x,0) and i(x,0) respectively. Then we perform Laplace transformation for Eq.(3) and (4).
02
222
02
222
∂
∂)0,(
∂
∂)0,(
t
t
t
ixsi
dx
IdcIs
t
vxsv
dx
VdcVs
-
-
For the case of initial values are zero. (or v(x,0)=0 and i(x,0)=0 )
scxscx
scxscx
sxVsxVLCsxI
sxVsxVsxV
)(2
)(1
)(2
)(1
),(),({=),(
),(+),(=),(
--
-
(7)
(8)
(9)
Eq.(9) is equivalent to Eq.(5) and Eq.(6).
In the Eq.(9), V1 and V2 are decided by boundary condition of the x. When a voltage source e(t) is connected at x=0, The Laplace transformation of e(t) is written as, L{e(t)}=E(s). For a current source i(t), it is also as, L{i(t)}=I(s).
Those are, at x=0, the voltage source e(t) is connected; V(0,s)=E(s) at x=0, the current source i(t) is connected; I(0,s)=I(s)The length of the transmission line is “ l ” at x=l, the terminal is shorten; V(l,s)=0 at x=l, the terminal is open; I(l,s)=0 at x=l, Z(s) is connected; V(l,s) / I(l,s)=Z(s)
For example, a voltage source e(t) with internal impedance Z0(s) are connected at x=0 as shown in Fig. The conditional equation is,
),0()()(),0( sIsZsEsV 0-
Terminal is shorted-circuit as in Fig. A electromotive force is connected at x=0, and the terminal at x=l is shortened. The boundary condition is, at x=0 ; V(0,s)=E(s) at x=l ; V(l,s)=0
From Eq.(9) first,
0),(
)}({)(),0()/(
2)/(
1
21
sclscl VVslV
teLsEVVsV
-
We can solve Eq.(10) for V1 and V2, and substitute them to Eq.(9), the Laplace transform of the voltage v and current I is calculated as,
(10)
)(+1=),(
)(=),(
)/()/(
)/)(()/)((
)/()/(
)/)(()/)((
sEWsxI
sEsxV
sclscl
scxlscxl
sclscl
scxlscxl
-
---
-
---
-
--
CLW =
(11)
(12)Here, (characteristic impedance)
After rearrangement of the Eq.(11), then expand it in a series,
)
()(
1
1)()(),(
)/)4(()/)4((
)/)2(()/)2(()/(
)/2()/)(()/)(()/(
--
-
--
-―-
-―--
-――-
scxlscxl
scxlscxlscx
sclscxlscxlscl
sE
sEsxV
By the same procedure, we can get the I(x,s) as,
)
)()(1
),(
)/)4(()/)4((
)/)2(()/)2(()/(
scxlscxl
scxlscxlsclsEW
sxI
-―-
―-―--
)4
()4
()2
()2
()({1
),(
)4
()4
()2
()2
()(),(
c
xlte
c
xlte
c
xlte
c
xlte
c
xte
Wtxi
c
xlte
c
xlte
c
xlte
c
xlte
c
xtetxv
-------
---
----
---
By inverse Laplace transformation
(13)
(14)
(15)
Terminal is shorted-circuit “For intuitive understanding”
Response for step voltage function (Opposite phase reflection)
Terminal is shorted-circuit
Response for step current function (Same phase reflection)
Terminal is open circuit as in Fig. A electromotive force is connected at x=0, and the terminal at x=l is opened. The boundary condition is,
0(1
),(
)(),0(
)/(2
)/(1
21
)-- sclscl VVW
slI
sEVVsV
We can solve Eq.(16) for V1 and V2, and substitute them to Eq.(9), the Laplace transform of the voltage v and current I is calculated. Then expand it in a series and next by inverse Laplace transformation, we can get v(x,t) and i(x,t) as,
(16)
})4
()4
()2
()2
()({1
),(
)4
()4
()2
()2
()(),(
---
----
---
--
-----
--
c
xlte
c
xlte
c
xlte
c
xlte
c
xte
Wtxi
c
xlte
c
xlte
c
xlte
c
xlte
c
xtetxv
(17)
Terminal is open-circuit
Response for step voltage function (Same phase reflection)
Terminal is open-circuit
Response for step current function (Opposite phase reflection)
)(=+
=),(),(
)(=+=),0(
)/(2
)/(1
)/(2
)/(1
21
sZVV
VVWslI
slV
sEVVsV
sclscl
sclscl
--
-
Here, we set Z(s)=R for the simplicity. W is the characteristic impedance.
Z(s) is connected to the terminal. The boundary condition is,
WZ
WZr
For Z = 0, the terminal is shorted circuit. r = -1
For Z = ∞, the terminal is open circuit. r = 1
“reflection coefficient”
Opposite phase reflection
Same phase reflection
Sum of the “go” and “return” waves
Sum of the “go” and “return” waves
“Intuitive understanding”
Combined bump-septum magnet system for negative-positive ion injection
Structure of combined bump-septum magnet
Magnetic field of the combined bump-septum magnet
How to get a steep septum magnetic field
Measured value of magnetic field
Change of the bump magnet field by exciting the septum magnet
0.98
0.985
0.99
0.995
1
1.005
1.01
1.015
1.02
180 200 220 240 260 280 300 320 340
Change of the bump magnetic field by exciting the septum magnet
Bump-ON, Septum-ONBump-ON, Septum-OFF
B/B
0
x (mm)
Septum conductor
Normalization point(Center of bump magnet)
B=B0
Figure of combined bump-septum magnet
Figure of combined bump-septum magnet
Mechanical structure of the combined bump-septum magnet
Magnetic field distribution of “Normal septum”and “Combined septum”
-1.5
-1
-0.5
0
0.5
1
1.5
Magnetic field distribution of "Normal seputum" and "Combined septum"
B/B
0
X (cm)
Leakage flux
0-5 5
Combined septum (B0=0.775 T)
Normal septum (B0=0.729 T)
Comparison of “Normal septum”and “Combined septum”
Power supply system for the H-injection bump magnets
Power supply system for the combined bump-septum magnet system
Current waveform of the combined septum conductor
(Superimpose rectangular waves)
20μs/div, 5V/div (1kA/V)(a); Septum current(b); Main bump current
DESIGN OF THE MAGNETIC FIELD
(For 400-MeV Injection)
• In the upstream of the stripping foil The maximum magnetic field is estimated to be 0.55 T The beam loss rate is less than 10-6
The injection beam power is 133 kW Losses by Lorentz stripping is less than 1.3 W
• In the downstream of the stripping foil The magnetic field of the bump magnet is set to be about 0.2 T. Excited H0 with a principal quantum number of n ≥ 6 becomes the uncontrolled beam Yield of n ≥ 6 is 0.0136 The total H0 beam power is 0.4 kW The maximum uncontrolled beam loss is about 6 W
The magnetic field at the foil is designed to be less than the value at which the bending radius of the stripped electrons is larger than 100 mm.
Injection beam line (Horizontal)
• Injection line – Lorentz stripping loss
• 0.14W/m (B<0.45T)
– H0,H- beam • 0.4kW
(exchange efficiency 99.7%)
– Excited H0 loss• 5.5W (n6)
• H- beam and H0 beam are exchanged to H+ beam by two 2nd foils ”A&B”– Lead to beam dump– 0.4kW
0.2T<0.45T
2nd foil “A”
2rd foil”B”
0.4kWMain foil(99.7%)
Schematic Layout of Beam Orbit at Painting Injection Start
Fixed Closed-Orbit Bump Magnets ”SB-I~SB-IV”
• Four dipole bump magnets named ”SB-I~SB-IV” are identical in construction and are powered in series to give a symmetrical beam bump.
• The dipoles are out of vacuum and ceramic vacuum chamber is included in the magnet gap.
• The structure of the magnet is composed of two-turn coils and window frame core made by laminated silicon steel cores of which thickness is 0.1 mm.
586
930
320540
Structure of the Split-type Bump Magnet
• The exitation current is supplied in the middle of the core trough the split to form a symmetrical distribution of magnetic field along the longitudinal direction.
• To insert the second foil • Symmetrical power supply for a symmetrical field distribution along the
longitudinal axis
The Waveform of Magnetic Field
s500attack time flat top time
s600release time
s100
flat top level(k0)
%5.00 kk
trigger
ns50jitter
%0.50kreversal
s50s552
curr
en
t
Beam injection
Fig.1 Current pattern of the power supply of the shift bump magnet in horizontal
Unquestioned
Horizontal painting bump magnets
• Two sets of bump magnet pairs in the upstream of the F quadrupole magnet and the downstream of the D quadrupole magnet.
• These four painting bump magnets will be excited individually.• To form a local closed orbit include the F and D quadrupole magnets
730
580
468
290
flat top time
s10050~ s550300~s500attack time decay time
s50
±5% ±1%
ns50jitter
•Ideal wave form K0{ 1-sqrt( t/τ)}•Design wave form k0 【 1+[sqrt(ε/τ)-sqrt{( t+ε)/τ}]/[sqrt{(τ+ε)/τ}-sqrt(ε/τ)] 】•Differentiation same as the above
0.5k0/[sqrt{(τ+ε)/τ}-sqrt(ε/τ)]/sqrt{( t+ε)/τ}/τ
flat top level(k0
%5.00 kk
curr
en
t
Permissible error of the ideal waveform
Beam injection
trigger
%0.50kreversal
Fig.2 Current pattern of the power supply of the painting bump magnet in horizontal
Unquestioned
Waveform of Horizontal Painting Bump Field
Vertical Painting Magnets
• In the vertical plane, two steering magnets are installed on the beam-transport line at a upstream point led by p from the foil.
• Painting injection in the vertical plane is performed by sweeping of the injection angle.
• Both correlated and anti-correlated painting injections are available by changing the excitation pattern of the vertical painting magnet
10
360
16040
0
attack time flat top time decay time
±1% ±5%
Unquestioned
s500release time
decay time
s50
flat top level(k0)%0.10 kk
±1%±5%
flat top times30
attack time
s550300~
s500 s30 s550300~
flat top level(k0)
%0.10 kk
ns50jitter
Unquestioned
Unquestioned
Beam injection
ns50jitter
Fig.2 Current pattern of the power supply of the painting bump magnet in vertical
Waveform of Vertical Painting Bump Field