J.B. Rosenzweig and Scott AndersonUCLA Dept. of Physics and Astronomy

ICFA Sardegna, July 2002

The Role of Space-charge in Emittance Measurement of High-brightness Photoinjector Beams

04/24/23 Rosenzweig/Anderson ICFA Sardegna 2002 2

Measuring the emittance of photoinjector beams

The low emittance of, and huge forces (internal and external) applied to these beams makes them behave very differently (like plasmas) than emittance dominated beams

In addition, investigation of the behavior of these beams, as well as optimization of the beam’s end use, requires accurate measurement of the beam emittance

In order to produce accurate measurements, the emittance diagnostic must take into account the nature of photoinjector beams

04/24/23 Rosenzweig/Anderson ICFA Sardegna 2002 3

Measuring Emittance Traditional emittance measurement techniques (e.g. quadrupole scan)

use the envelope equation for a drifting beam ignoringignoring space-charge,

For typical photo-injector beams, this exclusion of the space-charge term is not appropriate except in a strongly focused waist. We see that these beams are space-charge dominated by the ratio of the space-charge to emittance terms in the full envelope equation.

We used the LLNL/UCLA Thomson scattering photoinjector, with a short pulse, low energy beam to test different emittance measurement techniques.

′ ′ σ x = εn2

γ 2σx3

R = 2Iσ02

γI0εn2 >>1

+ Iγ 3I0 σx +σy( )

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

04/24/23 Rosenzweig/Anderson ICFA Sardegna 2002 4

Slit Based Emittance Measurement

Beam phase spacephase space is reconstructed from the position and width of the beamlets on screen. Emittance calculated from phase space picture.

Collimation makess emittance dominated beamlet — expansion due to emittance, not space-charge. Plasma wavelength same; function becomes much smaller.

Rbeamlet=2

3πI

γIo

dεn

⎛ ⎝ ⎜

⎞ ⎠ ⎟

2<<1 βbeamlet

β ∝ dσ

⎛ ⎝ ⎜ ⎞

⎠ ⎟ 2

04/24/23 Rosenzweig/Anderson ICFA Sardegna 2002 5

Quadrupole Scan Measurements

Neglecting space chargeNeglecting space charge we can write an equation for 2 based on the Twiss parameters of the beam.

The procedure then, is to measure 2 (the mean square beam size)(the mean square beam size) versus the focal length of the lens and fit the resulting curve to calculate the emittance. Thick lens treatment often necessary in compact beamlines.

σ22 =ε β1−2α1L +L2γ1( ) −ε

f 2Lβ1−2L2α1( ) + εf 2 L2β1( )

LThin LensFocal Length fScreen

04/24/23 Rosenzweig/Anderson ICFA Sardegna 2002 6

Experimental Procedure

Emittance was measured using both the quad scan and slits for different beam plasma frequencies. The plasma frequency was changed by changing the laser

pulse length. This was done by altering the grating pair separation in the laser system.

For each set of measurements, the laser spot size and energy, grating pair separation, beam charge, and injection phase were recorded in order to calculate the plasma frequencies.

Quadrupole

Slits

YAG Screen

04/24/23 Rosenzweig/Anderson ICFA Sardegna 2002 7

Quad Scan Vs Slit Data

0

5

10

15

20

0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

Slit EmittanceQuad Scan Emittance

kp L

d

The strength of the space-charge forces are parameterized in the scan by product drift length between quadrupole and detector and the plasma

wave number.

04/24/23 Rosenzweig/Anderson ICFA Sardegna 2002 8

Simulation of the Quad Scan

Given the measurements of charge and laser pulse dimensions, we simulated the beam dynamics up to the quadrupole using PARMELA and HOMDYN.

The quad scan procedure was then simulated with PARMELA using point to point space charge, HOMDYN, and by integrating the envelope equation.

All three methods gave similar results. Linear transport models agreeing with PARMELA leads us to believe non-linear space charge effects are unimportant.

04/24/23 Rosenzweig/Anderson ICFA Sardegna 2002 9

Quad Scan Simulation

0

5

10

15

20

0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

Slit Emittance

Simulated Quad Scan Emittance

Quad Scan Emittance

PARMELA

Emittance [mm mrad]

k

p

L

d

PARMELA simulations predict emittances in good agreement with slit measurements.

Simulated quad scans with emittances set by the slit measurements give higher output emittance values that agree reasonably with quad scan measurements.

04/24/23 Rosenzweig/Anderson ICFA Sardegna 2002 10

Space-charge in the Quad Scan

There are two relevant normalized numbers two parameterize space charge strength, one measuring drift length, and the other measuring emittance v. space charge.

The white plot points locate the positions of the experimental data. The normalized emittance used as input to the simulations was 5 mm mrad.

kp is a measure of the ratio of the space-charge to emittance forces at the quadrupole.

04/24/23 Rosenzweig/Anderson ICFA Sardegna 2002 11

Interplay of Space-charge and Emittance: Simulation

Data and simulation both show asymmetry about minimum spot size.

Asymmetry is due to different emittance forces. If waist is emittance dominated, then envelope looks very different before and after waist.

Asymmetry makes fitting to a parabola problematic.

0

0.2

0.4

0.6

0.8

1

1.5 10

-3

2 10

-3

2.5 10

-3

3 10

-3

3.5 10

-3

x2

[mm

2]

1/f [1/mm]

0

0.2

0.4

0.6

0.8

1

1.2

1 10

-3

2 10

-3

3 10

-3

4 10

-3

5 10

-3

6 10

-3

7 10

-3

σ

x2

[mm

2]

1/f [1/mm]

0

0.5

1

1.5

2

2.5

2 3 4 5 6 7

Emittance Included

Space-Charge Only

x

2

[mm

2

]

1/f [1/m]

04/24/23 Rosenzweig/Anderson ICFA Sardegna 2002 12

Summary of Emittance Measurement Techniques

Quad scans are ill-suited for highly space-charge dominated beams because the beam evolves under the influence of both space-charge and emittance effects.

Rules of thumb Quad scan data may not be valid if

Asymmetry in the data is an indicator of trouble.

kpLd >1 kpβ >1