Download - A new anode tip for the DC spark system
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