A new anode tip for the DC spark system

Robin Rajamäki1.7.2014

Problem definition

• Gap distance measured through capacitance in system 1

• Problems with previous tips:– Capacitance too low (hemispherical tip)– Sensitivity to small angular misalignments (flat tip)

Need a compromise between a large capacitance and a small sensitivity to angular misalignment.

Approach

• Parameters:– R = radius of anode tip– r = radius of curvature– α = angle of curvature– h = height of anode tip

• Design criteria:– ”Need 2-3 spots on the cathode surface for

experiments”

Approach• Design constraints:

1. Field drops (at least) 50 % 2 mm away from the point where the A and the C are closest to eachother

2. Field within 2 mm region remains unchanged for 10 deg misalignment

• Goal:– Find R and r that satisfy the above constraints

and maximize the capacitance!

Approach• Motivation for choosing 10 degrees

Note the the anode is untypically misaligned here!

Methods

1. Find R= f(α) for which the geometry within the critical region remains unchanged at a maximal misalignment of θ (constraint 2)2. Find R_opt = f(α_opt), which gives E(x = 2mm) = E0/2 (constraint 1)

R_opt, α_opt will maximize the capacitance and meet the design constraints.

Method

• Tools:– Simulation software• FEM modeling in Ansys Maxwell v. 15• Data analysis in Matlab

– Analytical models • Sphere close to infinite plate• Parallel plate capacitor• Used to approximate upper bounds of numerical

simulations

Results

• Solution boundaries

Boundaries of interest

Results

• Function satisfying constraint 2:R = f(α) = ,

Results

• Electric field magnitude at x = 2 mm for R(α)

R ≈ 20 mm

Results• Capacitance and change in capacitance for R(α)

Discussion• Optimal tip:– R ≈ 20 mm– α ≈ 23⁰

• 4 cm diameter may be impractically large...

... decrease R (= increase α) whilst keeping acceptible C and ΔC.

Discussion

• Alternative tip:

d = 1.3 mm, h = 1 mm

Discussion• Solution visualisation