100keV Gun Test Stand - trash.net Home - trash.netleemann/work/leg/tmeta040244_talk.pdf · · 2004-05-03PAUL SCHERRER INSTITUT LEG Project Simon C. Leemann, May 3 2004 1 100keV

LEG ProjectP A U L S C H E R R E R I N S T I T U T

Simon C. Leemann, May 3 2004 1

100keV Gun Test StandDesign and Parameter Study

Internal Note SLS-TME-TA-2004-0244http://slsbd.psi.ch/pub/slsnotes/


P A U L S C H E R R E R I N S T I T U T LEG Project

Topics

• Gun Geometries

• Parameter Studies

• Solenoid Field

• Diode Gap

• Bunch Charge

• Bunch Length

• Active Emitter Area

• Scaling Laws and Extrapolation

• Projected Emittance and Slice Emittance

• Conclusions



• Gun Geometries


• Solenoid Field

• Diode Gap

• Bunch Charge

• Bunch Length


• Scaling Laws Extrapolation


• Conclusions

Topics



The First Gun Design Suggestion

19 MV/m1.8.10-7 m.rad



Peak Electric Field Strength

-5.5e+07

-5e+07

-4.5e+07

-4e+07

-3.5e+07

-3e+07

-2.5e+07

-2e+07

-1.5e+07

-1e+07

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0.022

Pe

ak E

lectr

ic F

ield

Str

en

gth

[V

/m]

Anode Position [m]

MAFIA ResultsFit: f(x)=a+b/x



A Simplified Design

MATERIALS: 1,3,

!

0.000E+00 5.000E!022.500E!02

0.000E+00

3.000E!02

1.500E!02

FRAME: 1 20/04/04 ! 16:34:01 VERSION[V4.106] OO.DRD

CUT PLOT OF THE MATERIAL DISTRIBUTION IN THE MESH

OM!:4106

COORDINATES/M

FULL RANGE / WINDOW

R[ 0.0000, 0.030000]

[ 0.0000, 0.030000]

Z[ 0.0000, 0.050000]

[ 0.0000, 0.050000]

#2DPLOT

!MESHLINE= 1

CUT AT =CONST.

Z

R

+



Optimizing the Cathode Tilt Angle

6e-08

8e-08

1e-07

1.2e-07

1.4e-07

1.6e-07

1.8e-07

2e-07

2.2e-07

2.4e-07

2.6e-07

60 65 70 75 80 85 90 95

No

rma

lize

d T

ran

sve

rse

RM

S E

mitta

nce

[m

*ra

d]

Tilt Angle [deg]

Different Tilt Angles of the Cathode Electrode

At gun exit (40mm)

65º



0.000E+00 5.000E-022.500E-02

0.000E+00

3.000E-02

1.500E-02

FRAME: 3 20/04/04 - 16:34:01 VERSION[V4.106] OO.DRD

ELECTRIC FIELD STRENGTH IN V/M

OP-:4106

COORDINATES/MFULL RANGE / WINDOWR[ 0.0000, 0.030000] [ 0.0000, 0.030000]Z[ 0.0000, 0.050000] [ 0.0000, 0.050000]

#CONTOUR

SYMBOL: E

COMPONENT...: Z

FUNCTION MIN:-3.330E+07

FUNCTION MAX: 1.515E+04

PLOTTED MIN:-3.330E+07

PLOTTED MAX: 1.515E+04

PLOTTED STEP: 6.662E+05

INTERPOLATE.: 0

LOGSCALE....= 0

MATERIALS: 0,1,3,

Z

R

+

-3.33E+07 -2.50E+07 -1.66E+07 -8.31E+06 1.52E+04

The Resulting Improved Design

19 MV/m6.10-8 m.rad



• Gun Geometries


• Solenoid Field

• Diode Gap

• Bunch Charge

• Bunch Length




• Conclusions

Topics



• Cathode Potential: -100kV

• Active Emitter Radius: ract=100µm

• Pulse: Gaussian, cut-off at ±3σt, σt=20ps, Q≈-5.10-12C ( Î=100mA )

• Initial Energy: γ0=1.0001, initial divergence is set to zero

• Iris: riris=500µm

• Tracked Macro-Particles: N=20000

• Tracked Path: From the cathode surface at z0=1mm to the end of the drift section at z=342mm

Input Parameters



Input Geometry

MATERIALS: 1,3,21,22,

0.000E+00 7.000E-023.500E-02

0.000E+00

3.000E-02

1.500E-02


CUT PLOT OF THE MATERIAL DISTRIBUTION IN THE MESH

OM-:4106

COORDINATES/MFULL RANGE / WINDOWR[ 0.0000, 0.030000] [ 0.0000, 0.030000]Z[ 0.0000, 0.070000] [ 0.0000, 0.070000]

#2DPLOT

-MESHLINE= 1

CUT AT =CONST.

Z

R

+



• Gun Geometries


• Solenoid Field

• Diode Gap

• Bunch Charge

• Bunch Length




• Conclusions

Topics



Applying a Solenoid Field (1)




2.000E-02

4.000E-02

6.000E-02

8.000E-02

0.000E+00 2.000E-02 4.000E-02 6.000E-02 8.000E-02


MAGNETIC FLUX DENSITY IN TESLA

OP-:4106

#1DGRAPH

ORDINATE: BCOMPONENT: Z

FIXED COORDINATES:DIM...........MESHLINE R 1 - 1

ABSCISSA: GEOMETRY[BASE OF B]

REFERENCE COORDINATE: ZVARY..........MESHLINEFROM 1 TO 126




0

1e-07

2e-07

3e-07

4e-07

5e-07

6e-07

7e-07

8e-07

9e-07

1e-06

0 0.05 0.1 0.15 0.2 0.25 0.3

No

rma

lize

d T

ran

sve

rse

RM

S E

mitta

nce

[m

*ra

d]

z [m]

Solenoid Current Density Scaling (f=1.0 ~ 5.4A/mm^2 and on-axis Bz=85mT)

f=1.0f=0.0




0.0031

0.0032

0.0033

0.0034

0.0035

0.0036

0.0037

0.0038

0.0039

0 0.05 0.1 0.15 0.2 0.25 0.3

Sig

ma

z [

m]

z [m]

Solenoid Current Density Scaling (f=1.0 ~ 5.4A/mm^2 and on-axis Bz=85mT)

f=1.0f=0.0










2.4.10-8 m.rad

0

2e-07

4e-07

6e-07

8e-07

1e-06

1.2e-06

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

No

rma

lize

d T

ran

sve

rse

RM

S E

mitta

nce

[m

*ra

d]

Solenoid Current Density Scaling (1.0 ~ 5.4A/mm^2 and on-axis Bz=85mT)

At exit (34cm)




1e!08

2e!08

3e!08

4e!08

5e!08

6e!08

7e!08

8e!08

9e!08

0.1 0.15 0.2 0.25 0.3 0.35

No

rma

lize

d T

ran

sve

rse

RM

S E

mitta

nce

[m

*ra

d]

z [m]

Minimum Emittance vs. Longitudinal Position

MAFIA

f=1.05

f=1.10f=1.15

f=1.20

f=1.25

f=1.30



• Gun Geometries


• Solenoid Field

• Diode Gap

• Bunch Charge

• Bunch Length




• Conclusions

Topics



Varying the Gap (1)

11mm gap



Varying the Gap (2)

0

5e-08

1e-07

1.5e-07

2e-07

2.5e-07

3e-07

3.5e-07

4e-07

4 5 6 7 8 9 10 11

No

rma

lize

d T

ran

sve

rse

RM

S E

mitta

nce

[m

*ra

d]

Diode Gap [mm]

Diode Gap of 11mm Corresponds to 19MV/m Peak Field

30cm after anode tip, f=0.030cm after anode tip, f=0.530cm after anode tip, f=1.0

30cm after anode tip, f=1.05



• Gun Geometries


• Solenoid Field

• Diode Gap

• Bunch Charge

• Bunch Length




• Conclusions

Topics



Varying the Bunch Charge

0

5e-08

1e-07

1.5e-07

2e-07

2.5e-07

3e-07

3.5e-07

0 0.2 0.4 0.6 0.8 1

No

rma

lize

d T

ran

sve

rse

RM

S E

mitta

nce

[m

*ra

d]

Scaling Factor of 1.0 Corresponds to a Bunch Charge of ~5pC (~100mA Peak Current)


30cm after anode tip, solenoid f=0.0030cm after anode tip, solenoid f=0.5030cm after anode tip, solenoid f=1.0030cm after anode tip, solenoid f=1.05



• Gun Geometries


• Solenoid Field

• Diode Gap

• Bunch Charge

• Bunch Length




• Conclusions

Topics



Varying the Bunch Length

0

5e-08

1e-07

1.5e-07

2e-07

2.5e-07

3e-07

3.5e-07

1 2 3 4 5 6 7 8 9 10

No

rma

lize

d T

ran

sve

rse

RM

S E

mitta

nce

[m

*ra

d]

Scaling factor of 1.0 corresponds to a bunch length sigma of 20ps (~100mA peak current)


34cm after anode tip, solenoid f=0.0034cm after anode tip, solenoid f=0.5034cm after anode tip, solenoid f=1.0034cm after anode tip, solenoid f=1.05

~3 ~8



• Gun Geometries


• Solenoid Field

• Diode Gap

• Bunch Charge

• Bunch Length




• Conclusions

Topics



Varying the Active Emitter Radius

2e-07

2.2e-07

2.4e-07

2.6e-07

2.8e-07

3e-07

3.2e-07

1 2 3 4 5 6

No

rma

lize

d T

ran

sve

rse

RM

S E

mitta

nce

[m

*ra

d]

Active Emitter Radius Scaling

Scaling Factor of 1.0 Corresponds to an Active Emitter Radius of 0.1mm

At exit (34cm)

~2.5



• Gun Geometries


• Solenoid Field

• Diode Gap

• Bunch Charge

• Bunch Length




• Conclusions

Topics



The bare (but ugly) truth:

• The simulated bunch length ( ±3σz, σz=20ps ) is much lower than what we expect at the test stand

• However, it is necessary in order to observe the dynamics of the full bunch (MAFIA dumps phase space data at certain times, not at a certain location)

A possible solution:

» Can we simulate long bunches by inserting less charge into short bunches?

Scaling Parameters - Extrapolating Results



Bunch Lengthening vs. Reducing the Charge

0

5e!08

1e!07

1.5e!07

2e!07

2.5e!07

3e!07

3.5e!07

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Norm

aliz

ed T

ransvers

e R

MS

Em

itta

nce [m

*rad]

Sole

noid

Scalin

g F

acto

r

Scaling Factor

Pulse_length * 1/fCharge * f

f=1.05

f=1.00

f=0.50

f=0.00



• Gun Geometries


• Solenoid Field

• Diode Gap

• Bunch Charge

• Bunch Length




• Conclusions

Topics



ε =√〈r2〉〈pr

2〉 − 〈rpr〉2 $ γβ√〈r2〉〈r′2〉 − 〈rr′〉2

Transverse Normalized RMS Emittance

• Projected Emittance (property of one entire bunch)

• Slice Emittance (depends on the location t0 of the slice within the bunch and the width σt of the slice )

What is Slice Emittance?

εt0 = γβ√〈r2

t0〉〈r′t0

2〉 − 〈rt0 r′t0〉2



= e− (zi−z0)2

2β2c2σ2

How do we calculate Slice Emittance?

wi,0 = e−(ti−t0)2

2σ2

W0 =N∑

i=1

wi,0

〈r2t0〉 =

1W0

N∑i=1

ri2 · wi,0



Slice Emittance Example

σz = 0.3 mm



• Gun Geometries


• Solenoid Field

• Diode Gap

• Bunch Charge

• Bunch Length




• Conclusions

Topics



Conclusions (1)Gun Design:

• We’re able to maintain a peak electric field strength < 20 MV/m

• By choosing a proper cathode electrode tilt angle we’ve managed to reduce the norm. transv. emittance to 6.10-8 m.rad

• By closing the gap between the electrodes the emittance can be further minimized to levels well below 10-8 m.rad

» How far will material and vacuum conditions allow us to go?

Solenoid:

• Using a properly tuned solenoid the emittance can be minimized at a certain location of interest

• Currently the minimum achieved norm. transv. emittance at the exit of the structure (z = 34 cm) is 2.4.10-8 m.rad



Conclusions (2)Bunch Charge:

• The amount of charge inserted into the bunch scales the emittance roughly linear if we have properly tuned solenoid focussing

Bunch Length:

• Without solenoid focussing lengthening the bunch leads to lower emittance

• With solenoid focussing there is a bunch length that minimizes emittance

Active Emitter Area:

• For a given anode iris radius there is an optimum active emitter radius

• For a given FEA the ratio of active emitter radius and anode iris radius can be optimized for minimum emittance



Conclusions (3)Extrapolating Results:

• In general we can not extrapolate exact results for longer bunches, but we can estimate upper limits for ε

• This has to do with the fact that our bunches are neither disk-shaped nor cigar-shaped, but rather between these two limits where the space charge forces depend strongly on the bunch geometry (ratio between bunch length and radial bunch envelope)

Slice Emittance:

• We can calculate slice emittance values for a bunch and compare with the projected emittance, but parameters have to be properly chosen due to the trade-off between numerical noise and possible resolution

• As expected the slice emittance in the center of the bunch is much smaller than the projected emittance of the entire bunch

Documents

100keV Gun Test Stand - trash.net Home - trash.netleemann/work/leg/tmeta040244_talk.pdf · · 2004-05-03PAUL SCHERRER INSTITUT LEG Project Simon C. Leemann, May 3 2004 1 100keV