Sergey Antipov Argonne Wakefield Accelerator group Z. Insepov, V. Ivanov The Direction of the E-field in Glass Pores

outline The direction of the E-field ~Collective effects ~Edge effects 2 ground Cathode, 2.5 kV 2 kV

Simulation Geometry 2000 V terminal Vacuum Glass substrate, ε = 5.8 Resistive coating, ε = 6.8 and σ = 1e-8 S/m (to get 10sMΩ per 5·10 6 pores) The pore has a 40μ diameter and 40:1 aspect ratio Resistive coating is 1μ thick 2000 V terminals are 20μ thick Simulation is full scale 3D Single pore at this point cathode ground cutout

Direction of the field in the pore Dielectric limit Conductive limit Div D = ρ, D = ε · E, E = - grad φ Div j = - ρ t, j = σ · E, E = - grad φ Pore coating has both: ε, σ In statics you solve one OR another. In reality the system starts in dielectric limit and progresses over time towards the conductive limit. Ex: capacitor

Time domain simulation (3D) Glass substrate, ε = 5.8 Resistive coating, ε = 6.8 and σ = 1e-8 S/m (to get 10sMΩ per 5·10 6 pores)

Field angle convergence to conductive limit ~ one second after voltage is turned on we reach conductive limit  Electric Field is parallel to the pore Except for the edge effects, sec

Electric field streamlines The voltage on the cathode is 2500V. MCP voltage is 2000V. Some field lines do not enter the pore. Edge effects Field alignment along the pore

Color: |E|; Arrows & streamlines: Electric field

Results ground Cathode, 2.5 kV 2 kV α We plot field orientation angle α along lines #1, 2, 3

Edge Effects in the pore The pore is screened: Angle restores quickly outside the pore Collective behavior is significant only near the edge! Edge effects are the most important 1 2 3

Collective effects far from edges (7 pores) Color: Angle=Atan(Ex/Ez); Streamlines in cross section - electric field

Collective effects far from edges (7 pores) Field orientation angle across the pores. No cross talk.

Very short to-do plan Collective + edge effects simulation Address mesh – memory limitation Geometry details ground Cathode, 2.5 kV 2 kV

summary Physics model is in place: field is parallel to the pore – Easy to change media parameters (ε, σ..) or voltages – Changing geometry is more work. I need a CAD drawing. – Computational challenges: mesh – memory limitation, singular points Look into a possibility to make an “effective” coating as a boundary condition Upcoming work – Collective - edge effects – REAL geometry Exact 2kV terminal geometry Round edges Ground plane geometry Your suggestions / requests