Selected Topics of Theory and Experiment on the Space- - - PowerPoint PPT Presentation

• Y. Zou

www.ireap.umd.edu www.ireap.umd.edu

Selected Topics of Theory and Experiment on the Space- Charge-Dominated Beam Physics

• Part I: general concepts of space-charge-dominated beams.

Outline

• Part II: University of Maryland Electron Ring(UMER) and its components.
• Diagnostics: BPM, energy analyzer …
• Part III: selected experimental and theoretical results
• Experimental study of beam energy spread evolution in intense

beam

• Theoretical study of beam emittance of a gridded

electron gun

• Experimental study of Resistive wall instability

Beam Transport in a Uniform Focusing Channel

Beam envelope equation:

3 2 2 "

= − − + R R K R k R ε

External focusing force Emittance

Beam 2a k0

2a

external focusing

2 3

K a a ε + Space charge + emittance Matched Beam:

2 2 3

• K

k a a a ε = +

Space charge force

) 1 ( 2

2 3 3 e

f I I K γ γ β − =

generalized perveance

Define intensity parameter (χ) χ = K a k0

2 2 = space charge force

external force k k0 1 = = − ν ν χ Betatron tune depression: ω ω χ

p

2 = Plasma frequency

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0

Intensity Parameter (χ) Existing rings HIF Drivers Intensity Parameter: χ =

2 2a

k K

O

Betatron Oscillations Curve 1 χ = − k k 2

P

ω χ ω = Plasma Oscillations Curve

Emittance Dominated Space-charge Dominated

λD >> a λD << a UMER Range

Space-Charge Dominated vs Emittance Dominated

University of Maryland Electron Ring

UMER designed to serve as a research platform for intense beam physics

• Beam Energy: 10 keV
• Beam current: 100 mA
• Generalized perveance 1.5 x 10-3
• Emittance, 4x rms, norm 10 micron
• Pulse Length 50 - 100 ns
• Bunch charge 5 nC
• Circumference 11.52 m
• Lap time 197 ns
• Tune Depression (k/k0) >0.15

• Fast Current Monitors (2+) (rise time < 200 ps)
• Beam Position Monitors (17 BPMs)
• Phosphor Screens (18+ P-Screens)

Diagnostics Available

• End Diagnostic Chamber:

–Energy Analyzer –Pepper-pot Emittance (Phase Space) Monitor –Slit-Wire Emittance (Phase Space) Monitor –Faraday Cup

UMER Diagnostics –BPM[1,2]

Right Electrode Left Electrode

Φ θ

Top Electrode Bottom Electrode

[1] Y. Zou etal, PAC 1999 [2] B. Quinn etal, PAC 2003

• 4
• 2

2 4 20 40 60 80

Relative Strength of Different Terms Electrode Angle (Degree) Sensitivity term Nonlinear term Coupling term

3 2 3

) / ( 20 b xy C b x B b x A V V Ln

L R

+       + =

C R1 I

s

F is chosen to be 76.99o to remove the coupling between X and Y direction [3].

[3] Y. Zou, Ph.D dissertation, UMD, 2000

UMER Diagnostics -BPM

Design of Energy Analyzer[1,2]

2nd Generation ~ 3 eV Resolution 1st Generation: Parallel-Plate Retarding EA > 20 eV Resolution Collimating Cylinder

• 10.13kV

Retarding Mesh

• 9999.5 V

10 keV Beam 3rd Generation: Res. < 1 eV Collector Grounded Housing

[1] Y. Zou, etal, Phys. Rev. ST Accel. Beams 5(7), 2002, p. 011502. [2] Y. Cui, Y. Zou etal, to submit to RSI.

0.2 0.4 0.6 0.8 1

5040 5050 5060 5070 5080 5090 Relative Particle Density Beam Energy (eV)

Curve I Curve II (a)

• Shift the measured mean energy towards low-energy side.

Longitudinal space-charge effect inside the Analyzer

• Measured rms energy spread are different

Problems: Parameters: 5 keV, 135 mA beam, Curve 1: 0.2 mA beam current inside the device Curve 2: 2.2 mA beam current inside the device

• Leave a large tail at the high-energy side.
• Make the FWHM of measured spectrum narrower than the

true spectrum

Potential solutions for thermal beam[1]

Beam energy: 5 keV, Initial beam energy spread: 10 eV (λ = Jin/Jlim)

• 5040
• 5020
• 5000
• 4980
• 4960

0.0160.018 0.02 0.0220.0240.0260.028 0.03 Potential (V) Distance (m)

Potential minimum

• f -5024.9 V

λ = 0.5

• 5000
• 4000
• 3000
• 2000
• 1000

0.005 0.01 0.015 0.02 0.025 0.03 Potential (V) Distance (m)

• 8 V
• 2000 V
• 4400 V
• 5000 V

λ = 1.4

• 5000
• 4000
• 3000
• 2000
• 1000

0.005 0.01 0.015 0.02 0.025 0.03 Potential (V) Distance (m)

• 100 V
• 2000 V
• 4100
• 5000 V

[1] Y. Zou etal, submitted Phys. Rev. ST Acc. Beam

0.2 0.4 0.6 0.8 1 5040 5050 5060 5070 5080 5090 Relative Particle Density Beam Energy (eV)

Curve I Curve II

(c)

1D Theory and simulation plus 2D correction

• Curve I: λ = 0.062, Erms= 2.2 eV,

FWHM = 5.1eV Curve II: λ = 1.2, Erms= 5.1eV, FWHM = 0.49 eV

Comparison of Simulation Results and Experiments

Experiment

• Curve I: 0.2 mA inside the device

(λ=0.062, estimated), Erms= 2.2 eV, FWHM=3.4 eV

• Curve II: 2.2 mA inside the device

(λ=0.8, estimated), Erms= 3.2 eV, FWHM=1.1 eV

Nominal Energy : 5 keV, Current: 135 mA

0.2 0.4 0.6 0.8 1

5040 5050 5060 5070 5080 5090 Relative Particle Density Beam Energy (eV)

Curve I Curve II (a)

Part III: Selected Physics Topics

• Experimental study of beam energy spread evolution in

intense beam

• Transverse beam emittance of a gridded electron gun
• Experimental study of Resistive wall instability

Experimental Study of Beam Energy Spread in Space-Charge-Dominated Electron Beam*

* Y. Zou etal, to submit to Phys. Rev. STAB

Energy Spread Growth in the Intense Electron Beam

• Longitudinal-transverse relaxation (intra beam scattering)[1]
• Long relaxation time

[1] See the reviews in Chapters 5 and 6 of M. Reiser, “Theory and Design of Charged Particle Beams”, John Willey & Sons, 1994.

( ) ( )

2 / 1 2 / 1

* * ~ / * ~ D a J a D I Erms ∆

• Scaling law for the energy spread due to the L-T relaxation:
• Longitudinal-longitudinal relaxation[2]
• Short relaxation time, ~ plasma period

[2] See, for instance, A. V. Aleksandrov et al. Phys. Rev. A, 46, 6628 (1992) 2 / 1 3 / 1 2 // //,

] ) / ( ) 2 [( qV qn C T k qV E

B rms

πε + = ∆

• Theoretical prediction for the longitudinal energy spread

including both effects is given by:

UMER

Phase I Experimental Setup

Phosphor screen image Typical EA Signal

• 140
• 120
• 100
• 80
• 60
• 40
• 20

20

• 50

50 100 150 Energy Analyzer Signal (mV) Time (ns)

Electron Gun

First Solenoid Energy Analyzer Diagnostic Chamber Feedthrough

Movable Phosphor Screen

1 1.5 2 2.5 3 2.5 3 3.5 4 4.5 5 5.5 Energy Spread (eV) Beam Energy (keV) 1 1.5 2 2.5 3 2.5 3 3.5 4 4.5 5 5.5 Energy Spread (eV) Beam Energy (keV)

Circular: Experimental results Triangle: Theory

Typical Energy Spread Measurement Results

UMER

Energy Spread vs Beam Energy at Different Particle Densities

1 1.5 2 2.5 3 2.5 3 3.5 4 4.5 5 5.5 Energy Spread (eV) Beam Energy (keV)

5 10 15 20 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Beam Envelope (mm) Distance (m)

EA Position

Beam envelope (5 keV)

Comparison of experimental results and theory

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Energy Spread (eV)

Distance (m)

EA Position

Calculated energy spread

Energy Spread at Different Beam Currents

Beam Energy : 5 keV, Sampled position: 60 nS

• 0.2

0.2 0.4 0.6 0.8 1 1.2 5050 5060 5070 5080 5090 Relative Particle Density

Retarding Voltage (V)

Beam current: 135 mA Energy spread: 2.1 eV Beam current: 13 mA Energy spread: 1.7 eV

5 10 15 20 25 20 40 60 80 100 Energy Spread (eV) Time (ns) 5 10 15 20 25 20 40 60 80 100 Beam Energy Spread (eV) Time(ns)

Beam current: 135 mA Beam current: 13 mA

Energy spread along the pulse (time resolved)

Figure: Schematic of a Grid Gun

Transverse Beam Emittance Growth in a Gridded Electron Gun[1]

Cathode Grid (Vg) Anode (Va)

dcg dca Electron beam

[1] Y. Zou etal, to appear in NIM

. 1 0.2 . 3 0.4 0.5 Distance from Cathode Hm mL 5 10 15 20 25 30 35 40

l a i t n e t

• P

HVL

Scenario I Scenario II Scenario III Grid

Potential Distribution at Different Grid Voltages

Cathode grid distance: dcg = 0.15e-3 m, dca = 0.027 m, Va = 10000V

Potential distribution

0.1 0.2 0.3 0.4 0.5 Distance from Cathode H mmL

• 200000
• 100000

100000

l a c i r t c e l E d l e i F

HV mL

Electrical field

( )

1/2 1/2 1 2

4 3

g z g g

V E c V c d ∆ = + +

Field discontinuity due to the non-natural grid potential

Emittance of Multi Beam Systems

x y

Configuration space Beam trace space

R

' m

X

'

x

x

1/2 , 2

2 ( ) 4

g z n g g

eV E GRa mc V ε ∆ =

1/2 3 2 2 2

16 1 4 3

N i N

G i i λ λ π

=−

  = −    

∑

Where is geometry factor Effective normalized emittance can be calculated as

Calculated Emittance Growth Vs. Grid Voltage

Cathode grid distance: dcg = 0.15e-3 m, dca = 0.0255 m, Beam radius: R = 4e-3 m Half opening of mesh: a = 0.075e-3 m, Anode Voltage: Va = 10000 V

Normalized effective emittance vs. grid voltage

5 10 15 20 25 30 Grid Voltage HVL 5 10 15 20 25 30

d e z i l a m r

• N

e v i t c e f f E e c n a t t i m E

H

d a r m m m

L

Compare with the Experimental Results

Calculation results:

• emittance due to grid: εn,g = 14 mm mrad
• emittance due to intrinsic thermal motion: εn,i = 3.5 mm-mrad
• emittance due to non-ideal gun focusing structure[1]:

εn,f =6 mm mrad

• Total calculated emittance: ~ 15. 6 mm-mrad

Cathode grid distance: dcg = 0.15e-3 m, dca = 0.0255 m, Beam radius: R = 4e-3 m Half opening of mesh: a = 0.075e-3 m, Anode Voltage: Va = 10000 V, Grid Voltage: ~25 V

2 2 2 , , , n g n i n f

ε ε ε + + =

[1] D. Kehne, 10 KV Electron Gun Manual

Experimental results[2]:

12~16 mm-mrad

[2] S. Bernal, Internal report, IREAP, 2000

3-D realistic PIC simulation with WARP? - I. Haber

Experiments on Resistive-wall Instability in Space-Charge- Dominated Electron Beam [1,2]

[1] Y. Zou etal, Phys. Rev. Lett., Vol. 84, p 5138(2000) [2] H. Suk, J.G. Wang, Y. Zou, etal J. Appl. Phys. Vol. 86, No. 3, p 1699 (1999)

Iw Bθ(z) Beam Current C* C* R* L* Er(z)

Linear Theory

In one-dimensional theory, the resistive-wall instability is governed by following two linearized equations: and

) , ( ) , (

1 1

= ∂ ∂ + ∂ Λ ∂ z t z i t t z

p p f t z qE t p z f p qE z v t ∂ ∂ − =         ∂ ∂ + ∂ ∂ + ∂ ∂ ) ( ) , ( ) , , (

1 1

) ( z k wt i z k

r i e

e

± ±

k R e gm

i w

=

*

πε γ Λ

In the long-wavelength range (λ>>d), the resistive-wall instability solution can be expressed as: with

Experimental Apparatus(1)

EA PS EM Computer CCD Camera Short Solenoid

Generation of Space-Charge Waves[1]

Fast wave has positive current perturbation

Cathode-Grid pulse (velocity perturbation)

• 1
• 0.8
• 0.6
• 0.4
• 0.2
• 20

20 40 60 80 100 120 140 Voltage (V) Time(ns)

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

• 20

20 40 60 80 100 120 140 Beam Current (Normalized) Time(ns)

Fast wave

(a)

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

• 20

20 40 60 80 100 120 140 Beam Current (Normalized) Time(ns)

Slow wave

(b)

Slow wave has negative current perturbation

[1] J. G. Wang and M. Reiser, Rev. Sci. Instrum., 65(11), 3444 (1994).

• 280
• 240
• 200
• 160
• 120
• 80
• 40

20 30 40 50 60 70 80 90 100 Time(ns) ∆V=0 V ∆V=5 V ∆V=8 V ∆V=11 V ∆V=17 V ∆V=21 V

• 70
• 60
• 50
• 40
• 30
• 20
• 10

80 90 100 110 120 130 140 Time(ns) ∆V=0 V ∆V=3 V ∆V=7 V ∆V=9 V ∆V=11 V ∆V=13 V

Linear Results for Fast Waves

After the resistive wall Before the resistive wall

Fast wave decays in the resistive-wall pipe. DE1=21eV, DE2=13 eV, decay rate ki= -0.48 /m Beam energy: 3.5 keV, Beam current: 19.8 mA

Linear Results for Slow Waves

Slow wave grows in the resistive-wall pipe. DE1=27eV, DE2=37 eV, growth rate ki= 0.32/m Beam energy: 2.5 keV, Beam current: 30 mA

• 600
• 500
• 400
• 300
• 200
• 100

100 20 40 60 80 100 120 140 Energy Analyzer Signal (mV) Time(ns) ∆V=0 V

(a)

∆V=5 V ∆V=10 V ∆V=15 V ∆V=20 V ∆V=27 V

• 160
• 140
• 120
• 100
• 80
• 60
• 40
• 20

80 100 120 140 160 180 200 Energy Analyzer Signal(mV) Time(ns)

(b)

∆V=0 V ∆V=5 V ∆V=10 V ∆V=20 V ∆V=25 V ∆V=30 V ∆V=37 V

Before resistive wall After resistive wall

Fast Wave Decay Rate at Different Beam Energies

Beam Energy (keV)

2.5 3.5 4

Beam Current (mA)

15.6 19.8 23.2

∆E1 (eV)

12 ± 1 21 ± 1 18 ± 1

∆E2 (eV)

7 ± 1 13 ± 1 16 ± 1

Experimental ki (1/m)

• 0.54 ± 0.2
• 0.48 ± 0.12
• 0.12 ± 0.12

Calculated ki from Eq.(3.21) (1/m)

• 0.41
• 0.4
• 0.39

Large Perturbation (Nonlinear Regime)

• 0.2

0.2 0.4 0.6 0.8 1

• 20

20 40 60 80 100 120 140 Beam Current(normalized) Time(ns)

perturbation

Ip Ib

Example of a nonlinear initial current perturbation. perturbation strength = Ip/Ib

In the nonlinear regime, energy width of particles associated with fast wave increases. DE1=20 eV, DE2=25eV, Ki = 0.23 1/m Beam energy 2.5 keV, Beam current 16 mA

• 50
• 40
• 30
• 20
• 10

10 20 30 40 50 60 70 80 90 100 Fast wave signal at EA1 Time(ns)

∆V=0 V ∆V=2V ∆V=12 V ∆V=7 V ∆V=20 V

• 60
• 50
• 40
• 30
• 20
• 10

10 80 90 100 110 120 130 140 150 Fast wave signal at EA2 Time(ns)

∆V=0 V ∆V=3 V ∆V=13 V ∆V=8 V ∆V=18 V ∆V=25 V

Fast Wave in the Nonlinear Regime

After the resistive wall Before the resistive wall

Fast Wave Growth Rate vs Initial Perturbation Strength

Beam energy 2.5 keV, Beam Current 16 mA.

• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Growth Rate (1/m) Perturbation Strength

Summary

• Overview of UMER and its design and diagnostics
• Design of BPM and Energy analyzer
• Experimental study of beam energy spread in the intense

electron beam

• Beam emittance growth in a gridded electron gun
• Experimental study of resistive wall instability