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