Contents

Coil sizing analysis

Amperium wire: Type 8502-350, copper laminated Ic is 350 A at 77K, 700 A at 30 K. copper clad with thin ribbon of YCBO inside. YCBO may be just 1 micron. 0.18 to 0.22 mm thick and 12 mm wide. SuperPower: 2nd generation HTS tapes are 1/2 thickness of competitors; SCS12050 is 12 mm wide and 0.1 mm thick, 0.04 mm of which is copper & 0.05 mm Hastelloy C-276; 300 A at self-field Supercon LTS: NbTi: Ic is 350 A for 2:1 Cu/SC wire at 0.7 mm diameter and 700 A for 1.04 mm diameter at 5 T Nb3Sn: Ic is 500 A at 1 mm wire for 9 T (4.2 K) http://www.supercon-wire.com/content/nbti-superconducting-wires#MultiTable

Note: tapes and round wire will have different packing factors

See also: EllipsoidalSolenoid

%--------------------------------------------------------------------------

%--------------------------------------------------------------------------
% Copyright (c) 2016 Princeton Satellite Systems, Inc.
% All rights reserved.
%--------------------------------------------------------------------------

Magnet parameters

current = 1e6;   % for ~7 T see ConcentricCoils/MagneticFieldCurrentLoop
% at 50 cm, 5e6 A produces 6.28 T
% at 40 cm, 1e6 A produces 1.57 T
% at 30 cm, 1e6 A produces 2.09 T
% at 20 cm, 1e6 A produces 3.14 T
radius = 40;     % cm
useHTS = true;
conductor = 'Amperium-30K';
lts = 'NbTi-104';

switch conductor
  case 'Amperium-77K'
    tapewidth = 12;  % mm
    thickness = 0.2; % mm
    capacityYCBO = 350;  % A per wire (77 K, self-field)

  case 'SuperPower-77K'
    tapewidth = 12;  % mm
    thickness = 0.1; % mm;
    capacityYCBO = 300;  % A per wire (77 K, self-field)

  case 'Amperium-30K'
    % Amperium density approx 0.2 g/cm
    tapewidth = 12;  % mm
    thickness = 0.2; % mm
    capacityYCBO = 700;  % A per wire (30 K, ? T)
    % Note: this may be an underestimate of current based on lift factor graphs

  case 'SuperPower-30K'
    tapewidth = 12;  % mm
    thickness = 0.1; % mm;
    capacityYCBO = 1500;  % A per wire (30 K, 5T)

  case 'SuperPower-4K'
    % 30 um substrate tape at 4.2 K
    tapewidth = 4;    % mm
    thickness = 0.08; % mm
    capacityYCBO = 1000;  % A per wire (4.2 K, 5T)
end

switch lts
  case 'NbTi-070'
    % 0.7 mm wire carries 350 A at 5 T
    diameter = 0.7;     % mm
    capacityNbTi = 350; % A

  case 'NbTi-104'
    % 1.04 mm wire carries 700 A at 5 T
    diameter = 1.04;    % mm
    capacityNbTi = 700; % A
end
disp(conductor)
disp('------------')

Amperium-30K
------------

YCBO HTS tape

Amperium: 350 A at 77 K and 700 A at 30 K linear mass density (g/cm) if assume 100% copper

copper = 8.96; % g/cm3
disp('YCBO approx lineary density: (g/cm)')
rhoYCBO = copper*tapewidth*thickness/1e2

YCBO approx lineary density: (g/cm)
rhoYCBO =
      0.21504

NbTi alloy wires

NbTi: 0.268 to 0.286 lb/in3, equals 7.43 to 7.93 g/cm3 approx 0.04 to 0.06 g/cm 0.7 mm wire carries 350 A at 5 T 1.04 mm wire carries 700 A at 5 T

disp('NbTi approx linear density: (g/cm)')
NbTiWire = 7.4; % g/cm3
rhoNbTi = NbTiWire*pi*(diameter/20)^2

NbTi approx linear density: (g/cm)
rhoNbTi =
     0.062862

Choose for coil calculation

if (useHTS)
  density = rhoYCBO;
  capacity = capacityYCBO;  % A per wire
  disp('Using HTS')
else
  density = rhoNbTi;
  capacity = capacityNbTi;  % A per wire
  disp('Using LTS')
end

layers = ceil(current/capacity);
width  = layers*thickness*1e-3; % width if layers are stacked
massper = density*layers;

circ = 2*pi*radius;
mass = massper*circ*1e-3;  % coil mass to kg

fprintf('Current: %g A\n',current)
fprintf('Radius: %d cm\n',radius)
if (useHTS)
  fprintf('Conductor type: HTS\n');
else
  fprintf('Conductor type: LTS\n');
end
fprintf('Turns of wire: %d\n',layers)
fprintf('Single coil SC mass: %f kg\n',mass)
fprintf('Eight coil SC mass: %f kg\n',8*mass)

zC = [-1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75];
a0 = EllipsoidalSolenoid( 0.35, 0.5, zC )*100;
ellipsoidalMass = sum(massper*2*pi*a0*1e-3)


%--------------------------------------

Using HTS
Current: 1e+06 A
Radius: 40 cm
Conductor type: HTS
Turns of wire: 1429
Single coil SC mass: 77.230943 kg
Eight coil SC mass: 617.847547 kg
ellipsoidalMass =
       679.57

Published with MATLAB® R2020a