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A new anode tip for the DC spark system

A new anode tip for the DC spark system. Robin Rajamäki 1.7.2014. 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).

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A new anode tip for the DC spark system

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  1. A new anode tip for the DC spark system Robin Rajamäki 1.7.2014

  2. 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.

  3. 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”

  4. Approach • Design constraints: • Field drops (at least) 50 % 2 mm away from the point where the A and the C are closest to eachother • 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!

  5. Approach • Motivation for choosing 10 degrees Note the the anode is untypically misaligned here!

  6. Methods • Find R= f(α) for which the geometry within the critical region remains unchanged at a maximal misalignment of θ (constraint 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.

  7. 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

  8. Results • Solution boundaries Boundaries of interest

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

  10. Results • Electric field magnitude at x = 2 mm for R(α) R ≈ 20 mm

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

  12. 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.

  13. Discussion • Alternative tip: d = 1.3 mm, h = 1 mm

  14. Discussion • Solution visualisation

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