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## PowerPoint Slideshow about ' Fast orbit bump magnet' - hazina

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• 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

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.2

The critical damping of the circuit is given as,

The excitation current is given by next equation,

Fig.2 Principle of the circuit

Fast decay

1μs/div, 2V/div (50A/V)

Slow decay

Fig.3 Actual power supply circuit

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 recover

Voltage recover

Combination of LC resonant circuit and LR damping circuit

Principle of the circuit

Actual power supply circuit

2μs/div, 5V/div (1kA/V)

5μs/div, 5V/div (1kA/V)

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)

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 !

Parameters of H- injection bump magnet for the KEK Booster

Cross section of the core with “end–slit”

(0.1 mm Thick silicon steel, Nihon Kinzoku ST-100)

Iron loss

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)

Ladder-type

Line-type

Ladder-type

Rising phase of the wave form

Falling phase of the wave form

Pulse forming network for chicane bump magnets

(Using flattop field for injection)

PFN voltage, Magnet current and Magnet voltage

1ms/div, 5V/div (1kV/V)

50μs/div, 2V/div (1kA/V)

50μs/div, 0.5V/div

Fundamentals of Transmission Line Theory

“Exact transitional solution”

Let’s consider the part of transmission line as,

x

x + Δx

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.

Equations for v and i are given as,

finite difference equation.

(1)

Divide both sides by Δx and in the limit of Δx→0,

we can get next differential equations.

(2)

These simultaneous partial differential equations are known as “Telegraphy equation”

In the case of lossless transmission line,i.e. R = G = 0.

The telegraphy equation becomes

Here,

(3)

We can get wave equations. Here

(4)

The solution of Eq.(4) is given as,

(5)

v and i must satisfy the Eq.(3), we can get next solution for i,

(6)

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).

(7)

(8)

For the case of initial values are zero. (or v(x,0)=0 and i(x,0)=0 )

(9)

Eq.(9) is equivalent to Eq.(5) and Eq.(6).

In the Eq.(9), V1and 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,

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,

(10)

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,

(11)

(12)

Here,

(characteristic impedance)

After rearrangement of the Eq.(11), then expand it in a series,

(13)

By the same procedure, we can get the I(x,s) as,

(14)

By inverse Laplace transformation

(15)

“For intuitive understanding”

Response for step voltage function

(Opposite 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,

(16)

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,

(17)

Response for step current function (Opposite phase reflection)

Z(s) is connected to the terminal. The boundary condition is,

Here, we set Z(s)=R for the simplicity.

W is the characteristic impedance.

For Z = 0, the terminal is shorted circuit. r = -1

For Z = ∞, the terminal is open circuit. r = 1

“Intuitive understanding”

Same phase

reflection

Opposite phase

reflection

Sum of the “go” and “return” waves

Sum of the “go” and “return” waves

Magnetic field distribution of “Normal septum”and “Combined septum”

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 ofn ≥ 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

Main foil

(99.7%)

0.4kW

0.2T

<0.45T

2nd foil “A”

2rd foil”B”

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.

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

reversal

The Waveform of Magnetic Fieldcurrent

flat top level(k0)

Beam injection

Unquestioned

trigger

flat top time

attack time

release time

Fig.1 Current pattern of the power supply of the shift bump magnet in horizontal

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

reversal

Waveform of Horizontal Painting Bump Field

current

flat top level(k0

Permissible error of the ideal waveform

±1%

±5%

Beam injection

Unquestioned

trigger

attack time

flat top time

decay time

- 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

Fig.2 Current pattern of the power supply of the painting bump magnet in horizontal

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

jitter

Waveform of Vertical Painting Bump Field

flat top level(k0)

±1%

±5%

Unquestioned

attack time

flat top time

decay time

Unquestioned

flat top level(k0)

±5%

±1%

Unquestioned

Beam injection

decay time

attack time

flat top time

release time

Fig.2 Current pattern of the power supply of the painting bump magnet in vertical

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