Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Modulator Simulations and Prelim Dipole

Simulations

Jun Ma, Roman Samulyak, Kwangmin Yu

Department of Applied Mathematics and Statistics

Stony Brook University

2016.6.9

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

Ion moves with 1 βz along longitudinal direction

In the code, ion stays and electron bunch moves instead

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

Theory

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

Comparison

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

Theory

δE (zl)

E0=

< vz >

c

= − 1

en0πa2cId(γ0zl ,

Lmod

β0γ0c)

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

Theory

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

Theory

Formula is for a single ion in open space

We use superpositions of a series of ions along longitudinal

direction to model the periodic boundary

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

Comparison

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

rbore = 3cm, longitudinal number distribution

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

rbore = 3cm, longitudinal velocity distribution

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Fine MeshCoarse Mesh

Ion stays in the center

Uniform distribution for electrons

Periodic boundary

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Fine MeshCoarse Mesh

longitudinal number distribution

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Fine MeshCoarse Mesh

longitudinal velocity distribution

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Fine MeshCoarse Mesh√

v 2x + v 2

y along longitudinal

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Fine MeshCoarse Mesh

longitudinal number distribution

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Fine MeshCoarse Mesh

longitudinal velocity distribution

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Fine MeshCoarse Mesh√

v 2x + v 2

y along longitudinal

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

Electric field by ion is computed in open space

Use various computational domain size

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

8 Debye Length for domain size

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

16 Debye Length for domain size

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

32 Debye Length for domain size

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

80 Debye Length for domain size

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

8 Debye Length for domain size

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

16 Debye Length for domain size

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

32 Debye Length for domain size

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Density ModulationVelocity Modulation

80 Debye Length for domain size

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Magnetic field of dipoles

Bx(s) = B0 sin(kw · s)

By (s) = −B0 cos(kw · s)

kw = 2π/λw

λw = 4cm

B0 = 0.2T

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations

Moving IonModulator With Quadrupoles

Modulator With Uniform ElectronsIon In Open Space

Dipoles

Dipoles effect

Jun Ma, Roman Samulyak, Kwangmin Yu Modulator Simulations and Prelim Dipole Simulations