tfer_2C.m

% TFER_2C   Evaluates the transfer function for a PMA in Case D.
% Author:   Timothy Sipkens, 2019-03-21
% 
% Inputs:
%   sp          Structure defining various setpoint parameters 
%               (e.g. m_star, V). Use 'get_setpoint' method to generate 
%               this structure.
%   m           Particle mass
%   d           Particle mobility diameter
%   z           Integer charge state
%   prop        Device properties (e.g. classifier length)
%
% Outputs:
%   Lambda      Transfer function
%   G0          Function mapping final to initial radial position
%=========================================================================%

function [Lambda, G0] = tfer_2C(sp, m, d, z, prop)

[tau,C0] = parse_inputs(sp,m,d,z,prop);
        % parse inputs for common parameters

%-- Taylor series expansion constants ------------------------------------%
C3 = tau.*([sp.alpha]' .^ 2 .* prop.rc + ...
    2 .* [sp.alpha]' .* [sp.beta]' ./ prop.rc + ...
    [sp.beta]' .^ 2 ./ (prop.rc .^ 3) - ...
    C0 ./ (m .* prop.rc));
C4 = tau .* ([sp.alpha]' .^ 2 - ...
    2 .* [sp.alpha]' .* [sp.beta]' ./ (prop.rc .^ 2) - ...
    3 .* [sp.beta]' .^ 2 ./ (prop.rc .^ 4) + C0 ./ (m .* (prop.rc .^ 2)));
C5 = 2 .* tau .* (2 .* [sp.alpha]' .* [sp.beta]' ./ (prop.rc .^ 3) + ...
    6 .* [sp.beta]' .^ 2 ./ (prop.rc .^ 5) - C0 ./ (m .* (prop.rc .^ 3)));

C6 = -1 ./ (sqrt(4 .* C3 .* C5 - C4 .^ 2));

f = @(r) 2 .* C6 .* prop.v_bar .* ...
    atan(C6 .* (2 .* C5 .* (r - prop.rc) + C4));


%-- Evaluate G0 and transfer function ------------------------------------%
G0 = @(r) (tan((f(r) - prop.L) ./ ...
    (2 .* C6 .* prop.v_bar)) ./ C6 - C4) ./ (2.*C5)+prop.rc;

ra = min(prop.r2, max(prop.r1, G0(prop.r1)));
rb = min(prop.r2, max(prop.r1, G0(prop.r2)));

Lambda = real((1 ./ (2 .* prop.del)) .* (rb - ra));

end