7/23/20151 Relativistic electron beam transport simulation models German Kurevlev

7/23/20152 Developed models: three different models, single approach Ribbon (tape) beam, high conductivity, mainly for resistive hose instability (RHI) investigation Ribbon beam transport in different pressure gas investigations, including beam erosion and current enhancement Cylindrical beam with different current profile, resistive instabilities investigations (RHI plus filamentations for rotator)

7/23/ Ribbon beam, high conductivity (approximations) 1. High conductivity, 4πσ/c>>1, τ n = 1/4πσ << τ s = 4πσR 2 /c 2 2. Paraxial mono-velocity approximation V x <<V z or J b R<<I A =mc 3 γβ/q ~17kAγ, β = V z /c, γ = (1- β) -½, γ>>1, β~const 3. Small-angle Coulomb scattering with small energy transfer.

7/23/ Ribbon beam, high conductivity (equations) 1. 2 Bennett current profile for ribbon beams:

7/23/ Ribbon beam, high conductivity (scheme) PIC model (~1000 big particles) Tomas algorithm for fields Predictor-corrector 2 nd order absolutely stable scheme for particles dynamic Envelope equation good test correspondence demonstrated non-mixing beam z-segments z x x i i+1

7/23/ Ribbon beam, high conductivity (results) RHI theory similar to known cylindrical case was developed, including dispersion equation on the basic of several models (rigid beam, spread mass model, etc.) Computational results corresponds to the theory but additional normalization needed for real experiments. Frequencies with negative increment demonstrated. In real and computational experiment there are always unstable frequencies so two stages with negative and positive increment in RHI development found. Additional scattering effects demonstrated. Comparison with Nadezhdins work - RHI increment depends on length of scattering. Not quantitative due to different geometry.

7/23/ Ribbon beam in gas and plasma (approximations) No high conductivity approximation, could be σ*=4πσR b /c<<1 Paraxial mono-velocity approximation again V x <<V z or J b R b <<I A =mc3γβ/q ~17kAγ, β = V z /c, γ = (1- β) -½, γ -2 <<1, β~const 2. Small-angle Coulomb scattering with small energy transfer. 3. R b <<(cτ imp, c/ω)<<λ β =2πR b I A /J b

7/23/ Ribbon beam in gas and plasma (equations) Auto model fields equations (E.P.Lee) – one equation for a ribbon beam, see below. A=A z -φ Same particle dynamics and predictor-corrector technique so no new code needed for this part. Additional phenomenological equation for conductivity calculations

7/23/ Ribbon beam in gas and plasma (scheme) Similar to previous model but with more steps to get higher order field and conductivity values: PIC model Tomas algorithm for fields Predictor-corrector scheme for particles and conductivity with more steps (>=3) non-mixing beam z-segments z x x i i+1

7/23/ Ribbon beam in gas and plasma (results) Comparison with real beam transport in gas (Tomsk, under G.Sorokin supervising) with different pressure gave good qualitative results for middle and upper pressure range Erosion and current enhancement with RHI development demonstrated Stabilization on the first stage due to containing plasma channel generation

7/23/ Cylindrical beam (approximations) 1. Paraxial approximation V x <<V z or I b <<I A =mc3γβ/q ~17kAγ, β = V z /c, γ = (1- β) -½, γ -2 <<1, β~const R b <<λ β =π R b (2I A /I b ) ½ 2. Small-angle Coulomb scattering with small energy transfer 3. Investigated case - high conductivity, 4πσR/c>>1

7/23/ Cylindrical beam (scheme) Different beam current profiles: Bennett, rotator Cartesian coordinates but cylindrical channel with second order boundary conditions (similar to ribbon approach) Beam segments z x-y

7/23/ Cylindrical beam (results 1) Bennett current profile: Very good coincidence with dispersion equation (spread mass model) on linear stage Independent by X and Y axis RHI development on linear stage Current enhancement on non linear stage demonstrated Scattering effects on RHI with better coincidence that for ribbon beam demonstrated

7/23/ Cylindrical beam (results 2) Rotator beam profile: RHI instability investigated, theory was developed (Nadezhdin) to demonstrate that the beam width Δ is the parameter of the dispersion equation – in computational experiment it means that we will get the instability in any case due to the limit on the width linked with big particle size