Beam Dynamics Studies of CLIC DB Injector

Shahin Sanaye Hajari

1. Institute For Research in Fundamental Science (IPM), Tehran, Iran

2. CERN, Geneva, Switzerland

Contents

1. Introduction

2. Results of the Longitudinal Dynamics

3. Transverse Beam Dynamics Studies3.1 Envelop Equation

3.2 Emittance Growth

3.3 Simulations

1. Introduction 1

1. Introduction1.1 Injector Layout

2. Review of The Longitudinal Results 2

2. Review of The Longitudinal ResultsParameter Value Target valueRMS bunch length () 2.6 mm 3 mmRMS energy spread () 0.48 MeV < 0.5 MeVSatellite population 2.4 % < 5%Beam loss (chicane + satellite) 6.1 % As less as possible

3. Transverse beam dynamics studies 3

3. Transverse Beam Dynamics Studies3.1 Envelop Equation

𝑎′ ′+𝑘02𝑎− 𝐾𝑎 −

𝜖𝑡2

𝑎3 =0

Focusing term

Space charge term

Emittance term

𝑎=2𝑥𝑟𝑚𝑠

{ 𝑎′ ′ (0 )=𝑎′ (0 )=0

𝑘02𝑎− 𝐾𝑎 −

𝜖𝑡2

𝑎3 =0  Matched   Beam  

⇒𝐵=2𝛾𝑚𝛽𝑐

𝑒 √ 2𝑒𝐼4𝜋 𝜖0𝑚𝑐3 𝛽3𝛾 3𝑎2 +

𝜖𝑡2

𝑎4

3. Transverse beam dynamics studies 4

3. Transverse Beam Dynamics Studies3.2 Emittance Growth

𝑎′ ′+𝑘02𝑎− 𝐾𝑎 −

𝜖𝑡2

𝑎3 =0

𝜖𝑟𝑚𝑠=𝑥𝑟𝑚𝑠𝑥𝑟𝑚𝑠′ =𝑎

2

~𝑣𝑥

𝛽𝑐𝑇⊥=𝛾𝑚~𝑣𝑥

2

Sources of the emittance growth Non-stationary initial distribution Beam mismatching

3. Transverse beam dynamics studies 5

3. Transverse Beam Dynamics Studies3.2.1 Non-Stationary Initial Distributions

𝑛 (𝑟 )=𝑛(0)𝑒−𝛽2𝑐2𝑘0

2𝑟 2

2~𝑣𝑥2 −

𝑞𝜑 𝑠

𝑚𝛾3 ~𝑣𝑥2

1𝑟𝑑𝑑𝑟 (𝑟 𝑑𝜑𝑠

𝑑𝑟 )=− 𝑞𝜖0𝑛 (𝑟 )

Reiser’s formula:

Radial profile

3. Transverse beam dynamics studies 6

3. Transverse Beam Dynamics Studies3.2.2 Beam Mismatching

Wangler’s formula:

3. Transverse beam dynamics studies 7

3. Transverse Beam Dynamics Studies3.3 Simulations3.3.1 Beam Initial Conditions

𝑥𝑟𝑚𝑠=2𝑚𝑚𝜖𝑛=10𝑚𝑚−𝑚𝑟𝑎𝑑 PARMELA

3. Transverse beam dynamics studies 8

3. Transverse Beam Dynamics Studies3.3 Simulations3.3.2 Matched Beam

Magnetic field map

3. Transverse beam dynamics studies 9

3. Transverse Beam Dynamics Studies3.3 Simulations3.3.2 Matched Beam

RMS Beam Size RMS Normalised Emittance

3. Transverse beam dynamics studies 10

3. Transverse Beam Dynamics Studies3.3 Simulations3.3.2 Bunching Effect

𝐼𝑎𝑣=𝐼 0(𝐿𝑎𝑣 )0𝐿𝑎𝑣

Average bunch length

3. Transverse beam dynamics studies 11

3. Transverse Beam Dynamics Studies3.3 Simulations3.3.2 Bunching Effect

𝐼𝑎𝑣=𝐼 0(𝐿𝑎𝑣 )0𝐿𝑎𝑣

Average bunch current

3. Transverse beam dynamics studies 12

3. Transverse Beam Dynamics Studies3.3 Simulations3.3.2 Bunching Effect

Magnetic field map

Average current profile

3. Transverse beam dynamics studies 13

3. Transverse Beam Dynamics Studies3.3 Simulations3.3.2 Bunching Effect

RMS Beam Size RMS Normalised Emittance

Wangler’s formula:

3. Transverse beam dynamics studies 14

3. Transverse Beam Dynamics Studies3.3 Simulations3.3.2 Bunching Effect

Target beam size (mm) 2.0 2.5 3.0

21.5 24.1 33.3

Maximum magnetic field (G) 529 409 336

The larger the focusing field the smaller the beam size and the lower the emittance growth

3. Transverse beam dynamics studies 15

3. Transverse Beam Dynamics Studies3.3 Simulations3.3.3 Sensitivity to The Ideal Filed

3. Transverse beam dynamics studies 16

3. Transverse Beam Dynamics Studies3.3 Simulations3.3.3 Sensitivity to The Ideal Filed

RMS Beam Size RMS Normalised Emittance

𝛾𝛽𝜖  𝑟𝑚𝑠 (mm−mrad ) :24.1⟶24.8

Thanks for your attention