Forces between PCC and LTS for various axial distances

See also: CoAxRectangle, CoAxBField

Contents

%--------------------------------------------------------------------------
%    Copyright 2018 Princeton Satellite Systems, Inc. All rights reserved.
%--------------------------------------------------------------------------

oneWinding = false;
if oneWinding
  dzs = -0.35:0.02:0.35;
else
  dzs = 0:0.01:0.35;
end
forces = zeros(size(dzs));

for ind = 1:numel(dzs)

LTS facts

90A 0.5 T LTS magnet

  rLTSInner = 0.36/2;
  rLTSTurns = 16;
  zLTSTurns = 64;
  wireLTSR = 5e-4/2;
  dzLTS = 0.15;
  ILTS = 90;

Pulsed copper insert

AWG 4, 5.189 mm diameter, 500 ft spool, $480

  wireConductorCIR = 5.189e-3/2;
  wireWrappingCIR  = wireConductorCIR + 1.5e-3; % with 1.5mm of insulation
  rho              = 1.7e-8; % Ohm-m
  densityCopper    = 8.9e3;  % kg/m^3
  specificHeat     = 385;    % J/kg/K
  rCIInner = 0.094;          % 7.4 inch OD of spool
  rCITurns = 4;
  zCITurns = 39;
  dz = dzs(ind);

  % Insert derived quantities
  rCIMin = rCIInner;
  rCIMax = rCIInner + 2 * rCITurns * wireWrappingCIR;
  CILen1ZWinding = pi*(rCIMax^2 - rCIInner^2)/(2*wireWrappingCIR);
  CILenTot = CILen1ZWinding * zCITurns;
  CIMass = pi * wireConductorCIR^2 * CILenTot * densityCopper;
  R2 = CILenTot / (pi*wireConductorCIR^2) * rho;

  % Inductances
  [rCI,zCI] = CoAxRectangle(rCITurns,zCITurns,rCIInner,dz,wireWrappingCIR);
  % Two of these packs
  [rLTS1,zLTS1] = CoAxRectangle(rLTSTurns,zLTSTurns,rLTSInner,-dzLTS/2,wireLTSR);
  [rLTS2,zLTS2] = CoAxRectangle(rLTSTurns,zLTSTurns,rLTSInner,dzLTS/2,wireLTSR);
  if oneWinding
    rLTS = rLTS1;
    zLTS = zLTS1;
  else
    rLTS = [rLTS1;rLTS2];
    zLTS = [zLTS1;zLTS2];
  end

  % Currents
  % I2: current through the copper coil, I3: current induced in the LTS.
  I2 = 500; % A
  I3 = 0; % A

Calculate force

F = B*I*L

  Br = CoAxBField(rCI,zCI,rLTS,zLTS,ILTS); % B from LTS at positions of CI
  I  = I2*ones(size(rCI)); % Current of CI
  l  = 2*pi*rCI; % length of wire in CI

  forces(ind) = sum(sum(Br.*I.*l)); % N

end

Plots

Plot the resulting force per displacement in both English and metric units.

figure('name','Force in N');
plot(dzs,forces);
grid on;grid minor;
xlabel('Axial displacement (m)');ylabel('Force (N)');

figure('name','Force in lbf');
plot(dzs,forces/4.45);
grid on;grid minor;
xlabel('Axial displacement (m)');ylabel('Force (lbf)');


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Published with MATLAB® R2020a