Tw=2000;
MeshRarc = 5.45*10^-3;

%load('Saha_partition_functions.mat')

%CathModTe = if((x0-x)^2+(y0-y)^2< ArcRinner^2, 7000[K],if((x0-x)^2+(y0-y)^2>(1000*(ArcRouter^-2)^2.0/(7000-300))^(-1/2.0), 300[K], 7000[K]-(1000[K]/(ArcRouter^2)^2.0*((x0-x)^2+(y0-y)^2)^2.0)))
%CathModrhos2 = if((x-x0)^2+(y-y0)^2<(0.95*ArcRcylHS)^2, CathMod mi*0.1 [m^-3] *10^22, CathMod mi*1.0[m^-3] *10^22*exp(-((x-x0)^2+(y-y0)^2)^0.5*4.5/ArcRouter^1))

CathModTe_range = [3100:100:30000];
%for i=1:length(CathModTe_range)
%CathModTe = CathMode_range(i);

Tw_range=[1500:1:3200];
CathModq_range=[];
CathModj_range=[];
CathModjem_range=[];
CathModji_range=[];
CathModqem_range=[];
CathModqion_range=[];
CathModqrad_range=[];
CathModqtotal_range=[];


wf_range = [2.5, 25, 250, 2500, 25000, 100000];
%wf_range = [2500];
for k = 1:length(wf_range)

for i = 1:length(Tw_range)
    Tw=Tw_range(i);


CathModTe = 7000;
CathModrhos2 = 55.8*1.660539*10^-27*1*10^21;%if((x-x0)^2+(y-y0)^2<(0.95*ArcRcylHS)^2, CathMod mi*0.1 [m^-3] *10^22, CathMod mi*1.0[m^-3] *10^22*exp(-((x-x0)^2+(y-y0)^2)^0.5*4.5/ArcRouter^1))



ArcCurrent = 200; %[A];
ArcRcylHS = MeshRarc;
ArcRinner = 1*10^-3;%[mm]
ArcRouter = MeshRarc-1*10^-3; %[mm]
ArcVoltage = 26.9; % [V]
CathMode = 1.6 *10^-19; %[A s] 
CathModA = 4.6*CathMode; %[V]
CathModepsilon0 = 8.854187817 *10^-12; %[A s V^-1 m^-1] 
CathModEion = 7.9 *CathMode; %[V]
CathModTw=Tw;
CathModEmissivity = 0.39*exp(-(CathModTw-1810)/442)+0; 
CathModL = 349600; % [J/mol]
CathModNAvogadro = 6.022*10^23; %  [mol^-1] 
CathModPatm = 101000;%  [N/m^2]
CathModPplasma = 1.5*CathModPatm;
CathModR = 8.314; % [J/mol/K]
CathModmolarmass = 0.0558; % [kg mol^-1]
CathModRspec = CathModR/CathModmolarmass;
CathModTb = 3134; %[K]
CathModUD = 20; %[V]
CathModgamma = 5/3; 
CathModh = 6.626*10^-34; % [kg m^2 s^-1] 
CathModkB = 1.38*10^-23; %  [m^2 kg s^-2 K^-1] 
CathModme = 9.10938*10^-31; %  [kg]
CathModmi = 55.8*1.660539*10^-27; % [kg]
Tmelting = 1771; %. [K]


%(3),(4)
CathModPvap = exp(25.3456-4.2050*10^4/CathModTw);
omega = CathModPvap/wf_range(k);
CathModTplasmaLocal = (omega*exp(20.3417-4.205*10^4/CathModTw)+1.0168*10^3)/(omega/CathModTw*exp(20.3417-4.2050*10^4/CathModTw)+1.0168*10^3/CathModTe);



%(5)
p=[];
p(1)=1.5074*10^-21;
p(2)=-1.2955*10^-16;
p(3)=+4.2398*10^-12;
p(4)=-6.2329*10^-8;
p(5)=3.1937*10^-4;
p(6)=1.0658;
f1= p(1)*CathModTplasmaLocal^5+p(2)*CathModTplasmaLocal^4+p(3)*CathModTplasmaLocal^3+p(4)*CathModTplasmaLocal^2+p(5)*CathModTplasmaLocal^1+p(6);

%(6)
CathModSahakonstantf1 = f1* CathModTplasmaLocal^(3/2).*exp(49.9283-9.1594*10^4/CathModTplasmaLocal);

%(7)
CathModnisf1 = -CathModSahakonstantf1/2+CathModSahakonstantf1*sqrt((exp(79.3688-4.2050*10^4/CathModTw)/4/CathModTw+CathModrhos2)/(CathModSahakonstantf1)+1/4);
CathModnis = CathModnisf1;

%(8)
CathModji =  2.5208*10^-18*sqrt(CathModTplasmaLocal+CathModTw)*CathModnis;

%(9)
CathModAeff = 5.3333*10^4-0.0022*(CathModnis)^(1/4)*((CathModTplasmaLocal+CathModTw)*CathModUD)^(1/8);

%(10)
CathModjem = CathModTw^2*exp(13.997-CathModAeff/CathModTw); %[A/m^2] 

%(11)
CathModjtotal = CathModji+CathModjem;

%One Parameter
CathModjem_range(k,i)=CathModjem;
CathModji_range(k,i)=CathModji;

%(12)
CathModqem=CathModjem*(8.6250e-05*CathModTw+4.6);
%(13)
CathModqion = CathModji*(4.3125e-05*CathModTplasmaLocal+CathModUD+6.9284);
%(14)
CathModqrad = exp(-CathModTw/442-13.5321) * CathModTw^4;
%CathModqrad = 5.670367 * 10^-8 * CathModTw^4; %[W m^-2]
%(15)
CathModqtotal = CathModqion - CathModqem - CathModqrad;

CathModqem_range(k,i) = CathModqem;
CathModqion_range(k,i) = CathModqion;
CathModqrad_range(k,i) = CathModqrad; %[W m^-2]
CathModqtotal_range(k,i) = CathModqtotal;


CathModj_range(k,i)=CathModjtotal;
CathModq_range(k,i)=CathModqtotal;

%CathModq_bulk(i)
%CathModj_bulk(i)

end

end





%plot(CathModqem_range(4,:)./CathModjem_range(4,:))
%hold on
%plot(CathModqion_range(4,:)./CathModji_range(4,:))




legend_cell={};

k=length(wf_range);
%plot(Tw_range(CathModq_range(k,:)>0), CathModq_range(k,(CathModq_range(k,:)>0)), 'linewidth', 2, 'linestyle', '-')
plot(Tw_range, CathModq_range(k,:), 'linewidth', 2, 'linestyle', '-')

ylabel('q_{total} [W/m^{2}]', 'FontSize', 16)
xlabel('Cathode Surface Temperature T_{W} [K]', 'FontSize', 16)
xlim([min(Tw_range(CathModq_range(k,:)>0))-50 max(Tw_range(CathModq_range(k,:)>0))+50]);
ylim([-0.1*max(CathModq_range(k,:)) max(CathModq_range(k,:))+0.1*max(CathModq_range(k,:))]);
hold on
legend_print = sprintf('wf = %0.1e', wf_range(k));
legend_cell{k} = legend_print;


for k=1:length(wf_range)-1
   k=length(wf_range)-k;
plot(Tw_range(CathModq_range(k,:)>0), CathModq_range(k,(CathModq_range(k,:)>0)), 'linewidth', 2, 'linestyle', '-')
ylabel('q_{total} [W/m^{2}]', 'FontSize', 16)
xlabel('Cathode Surface Temperature T_{W} [K]', 'FontSize', 16)
%xlim([min(Tw_range(CathModq_range(k,:)>0))-50 max(Tw_range(CathModq_range(k,:)>0))+50]);
%ylim([0.5*min(CathModq_range(k, CathModq_range(k,:)>0)) max(CathModq_range(k,:))+500*max(CathModq_range(k,:))]);
hold on
legend_print = sprintf('wf = %0.1e', wf_range(k));
legend_cell{k} = legend_print;

end
legend_cell = flip(legend_cell)
legend(legend_cell, 'Location', 'northwest', 'FontSize', 16)
legend boxoff
sprintf("%i", CathModUD);
title(sprintf("U_{D}=%i[V]", CathModUD)+"; "+sprintf("T_{Plasma,bulk}=%i[K]", CathModTe)+"; "+newline+sprintf("n_{Fe,bulk}=%0.1e[m^{-3}]", CathModrhos2/CathModmi), 'FontSize', 12)
ax = gca;
ax.FontSize = 14
hold off



function [legend_h,object_h,plot_h,text_strings] = columnlegend(numcolumns, str, varargin)
%
%   columnlegend creates a legend with a specified number of columns.
%   
%   columnlegend(numcolumns, str, varargin)
%       numcolumns - number of columns in the legend
%       str - cell array of strings for the legend
%
%   Additional Input Options:
%   columnlegend(..., 'Location', loc)
%       loc - location variable for legend, default is 'NorthEast'
%                  possible values: 'NorthWest', 'NorthEast', 'SouthEast', 'SouthWest', 
%                                   'NorthOutside', 'SouthOutside',
%                                   'NortheastOutside', 'SoutheastOutside'
%
%   columnlegend(numcolumns, str, 'padding', 0.5); % add 50% vertical padding between legend entries (relative to original height)
%       
%   columnlegend(..., 'boxon')
%   columnlegend(..., 'boxoff')
%        set legend bounding box on/off
%
%   example:
%      plot(bsxfun(@times, [0:9]',[1:10])); 
%      columnlegend(3, cellstr(num2str([1:10]')), 'location','northwest');
%
%
%   Author: Simon Henin <shenin@gc.cuny.edu>
%   
%   4/09/2013 - Fixed bug with 3 entries / 3 columns
%   4/09/2013 - Added bounding box option as per @Durga Lal Shrestha (fileexchage)
%   11 May 2010 - 1.2 Add instructions for printing figure with columns
%   08 Feb 2011 - 1.4 Added functionality when using markers.
%   31 Oct 2015 - Updates for compatibility with 2015a, Adds minor improvements as per user suggestions
%   07 Nov 2016 - Bug fixes, added functionality for bar plots, added all valid legend locations 
%   07 Jun 2017 - Added a quick padding feature that creates additional
%   vertical space between legend entries.
location = 'NorthEast';
boxon = false; legend_h = false; padding = 0; extravars = [];
for i=1:2:length(varargin),
    switch lower(varargin{i})
        case 'location'
            location = varargin{i+1};
            i=i+2;
        case 'boxon'
            boxon = true;
        case 'boxoff'
            boxon = false;
        case 'legend'
            legend_h = varargin{i+1};
            i=i+2;
        case 'object'
            object_h = varargin{i+1};
            i=i+2;
        case 'padding'
            padding = varargin{i+1};
            i=i+2;
        otherwise
            extravars{end+1} = varargin{i};
            extravars{end+1} = varargin{i+1};
    end
end
if legend_h == false,
    %create the legend
    if ~isempty(extravars),
        [legend_h,object_h,plot_h,text_strings] = legend(str, extravars{:});
    else
        [legend_h,object_h,plot_h,text_strings] = legend(str);
    end
end
%some variables
numlines = length(str);
numpercolumn = ceil(numlines/numcolumns);
%get old width, new width and scale factor
set(legend_h, 'units', 'normalized');
set(gca, 'units', 'normalized');
pos = get(legend_h, 'position');
width = numcolumns*pos(3);
newheight = (pos(4)/numlines)*numpercolumn;
rescale = pos(3)/width;
%get some old values so we can scale everything later
type = get(object_h(numlines+1), 'type');
switch type,
    case {'line'}
        xdata = get(object_h(numlines+1), 'xdata');
        ydata1 = get(object_h(numlines+1), 'ydata');
        ydata2 = get(object_h(numlines+3), 'ydata');
        
        %we'll use these later to align things appropriately
        sheight     = ydata1(1)-ydata2(1) + (ydata1(1)-ydata2(1))*padding;          % height between data lines
        height      = ydata1(1) + (ydata1(1)-ydata2(1))*padding*2;                    % height of the box. Used to top margin offset
        line_width = (xdata(2)-xdata(1))*rescale;       % rescaled linewidth to match original
        spacer = xdata(1)*rescale;                      % rescaled spacer used for margins
    case {'hggroup'}
        text_pos    = get(object_h(1), 'position');
        child       = get(object_h(numlines+1), 'children');
        % determine if bar or errorbar
        subtype = get(child, 'Type');
        if strcmpi(subtype, 'patch'), % bar
            vertices_1  = get(child, 'vertices');
            child       = get(object_h(numlines+2), 'children');
            vertices_2  = get(child, 'vertices');
            sheight     = vertices_1(2,2)-vertices_1(1,2);
            height      = vertices_1(2,2);
            line_width  = (vertices_1(3,1)-vertices_1(1,1))*rescale;       % rescaled linewidth to match original
            spacer      = vertices_1(1,2)-vertices_2(2,2);                      % rescaled spacer used for margins
            text_space  = (text_pos(1)-vertices_1(4,1))./numcolumns;
        elseif strcmpi(subtype, 'hggroup'), % errorbar
            child1 = get(get(object_h(numlines+1), 'children'), 'children');
            child1 = child1(2);
            child2 = get(get(object_h(numlines+2), 'children'), 'children');
            child2 = child2(2);
            xdata = get(child1, 'xdata');
            ydata1 = get(child1, 'ydata');
            ydata2 = get(child2, 'ydata');
            %we'll use these later to align things appropriately
            sheight     = ydata1(1)-ydata2(1) + (ydata1(1)-ydata2(1))*padding;          % height between data lines
            height      = ydata1(1) + (ydata1(1)-ydata2(1))*padding*2;                    % height of the box. Used to top margin offset
            line_width = (xdata(2)-xdata(1))*rescale;       % rescaled linewidth to match original
            spacer = xdata(1)*rescale;                      % rescaled spacer used for margins
        end
end
%put the legend on the upper left corner to make initial adjustments easier
% set(gca, 'units', 'pixels');
loci = get(gca, 'position');
set(legend_h, 'position', [loci(1) pos(2) width pos(4)]);
col = -1;
for i=1:numlines,
    if (mod(i,numpercolumn)==1 || (numpercolumn == 1)),
        col = col+1;
    end
    
    if i==1
        linenum = i+numlines;
    else
        if strcmp(type, 'line'),
            linenum = linenum+2;
        else
            linenum = linenum+1;
        end
    end
    labelnum = i;
    
    position = mod(i,numpercolumn);
    if position == 0,
         position = numpercolumn;
    end
    
    switch type,
        case {'line'}
            %realign the labels
            set(object_h(linenum), 'ydata', [(height-(position-1)*sheight) (height-(position-1)*sheight)]);
            set(object_h(linenum), 'xdata', [col/numcolumns+spacer col/numcolumns+spacer+line_width]);
            
            set(object_h(linenum+1), 'ydata', [height-(position-1)*sheight height-(position-1)*sheight]);
            set(object_h(linenum+1), 'xdata', [col/numcolumns+spacer*3.5 col/numcolumns+spacer*3.5]);
            
            set(object_h(labelnum), 'position', [col/numcolumns+spacer*2+line_width height-(position-1)*sheight]);
        case {'hggroup'},
            if exist('subtype', 'var')&strcmpi(subtype, 'patch'),
                child = get(object_h(linenum), 'children');
                v = get(child, 'vertices');
                %x-positions
                v([1:2 5],1) = col/numcolumns+spacer;
                v(3:4,1) = col/numcolumns+spacer+line_width;
                % y-positions
                v([1 4 5],2) = (height-(position-1)*sheight-(position-1)*spacer);
                v([2 3], 2) = v(1,2)+sheight;
                set(child, 'vertices', v);
                set(object_h(labelnum), 'position', [v(3,1)+text_space v(1,2)+(v(2,2)-v(1,2))/2 v(3,1)-v(1,1)]);
            else
                child = get(get(object_h(linenum), 'children'), 'children');
                set(child(2), 'ydata', [(height-(position-1)*sheight) (height-(position-1)*sheight)]);
                set(child(2), 'xdata', [col/numcolumns+spacer col/numcolumns+spacer+line_width]);
                
%                 set(object_h(linenum+1), 'ydata', [height-(position-1)*sheight height-(position-1)*sheight]);
%                 set(object_h(linenum+1), 'xdata', [col/numcolumns+spacer*3.5 col/numcolumns+spacer*3.5]);
                
                set(object_h(labelnum), 'position', [col/numcolumns+spacer*2+line_width height-(position-1)*sheight]);
            end
    end
   
end
%unfortunately, it is not possible to force the box to be smaller than the
%original height, therefore, turn it off and set background color to none
%so that it no longer appears
set(legend_h, 'Color', 'None', 'Box', 'off');
%let's put it where you want it
fig_pos = get(gca, 'position');
pos = get(legend_h, 'position');
padding = 0.01; % padding, in normalized units
% if location is some variation on south, then we need to take into account
% the new height
if strfind(location, 'south'),
    h_diff = pos(4)-newheight;
    pos(4) = newheight;
end
switch lower(location),
    case {'northeast'}
        set(legend_h, 'position', [pos(1)+fig_pos(3)-pos(3)-padding pos(2) pos(3) pos(4)]);
    case {'northwest'}
        set(legend_h, 'position', [pos(1)+padding pos(2) pos(3) pos(4)]);        
    case {'southeast'}
        pos(4) = newheight;
        set(legend_h, 'position', [pos(1)+fig_pos(3)-pos(3)-padding fig_pos(2)-pos(4)/2+pos(4)/4 pos(3) pos(4)]);
    case {'southwest'}
        set(legend_h, 'position', [fig_pos(1)+padding fig_pos(2)-pos(4)/2+pos(4)/4 pos(3) pos(4)]);
    case {'northeastoutside'}
        % need to resize axes to allow legend to fit in figure window
        set(gca, 'position', [fig_pos]-[0 0 pos(3) 0]);
        set(legend_h, 'position', [pos(1)+fig_pos(3)-pos(3) pos(2) pos(3) pos(4)]);
    case {'northwestoutside'}
        % need to resize axes to allow legend to fit in figure window
        set(gca, 'position', [fig_pos]+[pos(3) 0 -pos(3) 0]);
        set(legend_h, 'position', [fig_pos(1)-fig_pos(3)*.1 pos(2) pos(3) pos(4)]); % -10% figurewidth to account for axis labels
    case {'north'}
        % need to resize axes to allow legend to fit in figure window
        set(legend_h, 'position', [fig_pos(1)+fig_pos(3)/2-pos(3)/2 fig_pos(2)+(fig_pos(4)-pos(4))-padding pos(3) pos(4)]);    
    case {'northoutside'}
        % need to resize axes to allow legend to fit in figure window
        set(gca, 'position', [fig_pos]-[0 0 0 pos(4)]);
%         set(legend_h, 'position', [fig_pos(1)+fig_pos(3)/2-pos(3)/2 fig_pos(2)+(fig_pos(4)-pos(4)) pos(3) pos(4)]);
        set(legend_h, 'position', [fig_pos(1)+fig_pos(3)/2-pos(3)/2 fig_pos(2)+fig_pos(4)-pos(4) pos(3) pos(4)]);
    case {'south'}
        y_pos = fig_pos(2)-h_diff+pos(4);
        set(legend_h, 'position', [fig_pos(1)+fig_pos(3)/2-pos(3)/2  y_pos pos(3) pos(4)]);
    case {'southoutside'}
        % need to resize axes to allow legend to fit in figure window
        set(gca, 'position', [fig_pos]-[0 -pos(4) 0 pos(4)]);
%         set(legend_h, 'position', [fig_pos(1)+fig_pos(3)/2-pos(3)/2 fig_pos(2)-pos(4)-pos(3)*0.1 pos(3) pos(4)]);
        set(legend_h, 'position', [fig_pos(1)+fig_pos(3)/2-pos(3)/2 0 pos(3) pos(4)]);
    case {'eastoutside'}
        % need to resize axes to allow legend to fit in figure window
        set(gca, 'position', [fig_pos]-[0 0 pos(3) 0]);
        set(legend_h, 'position', [pos(1)+fig_pos(3)-pos(3) fig_pos(2)+fig_pos(4)/2-pos(4)/2 pos(3) pos(4)]);
    case {'southeastoutside'}
        % need to resize axes to allow legend to fit in figure window
        set(gca, 'position', [fig_pos]-[0 0 pos(3) 0]);
        set(legend_h, 'position', [pos(1)+fig_pos(3)-pos(3) fig_pos(2)-pos(4)/4 pos(3) pos(4)]);
    case {'westoutside'}
        % need to resize axes to allow legend to fit in figure window
        set(gca, 'position', [fig_pos]+[pos(3) 0 -pos(3) 0]);
        set(legend_h, 'position', [fig_pos(1)-fig_pos(3)*.1 fig_pos(2)+fig_pos(4)/2-pos(4)/2 pos(3) pos(4)]); % -10% figurewidth to account for axis labels    
    case {'southwestoutside'}
        % need to resize axes to allow legend to fit in figure window
        set(gca, 'position', [fig_pos]+[pos(3) 0 -pos(3) 0]);
        set(legend_h, 'position', [fig_pos(1)-fig_pos(3)*.1 fig_pos(2)-pos(4)/4 pos(3) pos(4)]); % -10% figurewidth to account for axis labels        
end
% display box around legend
if boxon,
    drawnow; % make sure everyhting is drawn in place first.
%     set(legend_h, 'units', 'normalized');
    pos = get(legend_h, 'position');
    orgHeight = pos(4);
    pos(4) = (orgHeight/numlines)*numpercolumn;
    pos(2)=pos(2) + orgHeight-pos(4) - pos(4)*0.05;
    pos(1) = pos(1)+pos(1)*0.01;
    annotation('rectangle',pos, 'linewidth', 1)
end
% re-set to normalized so that things scale properly
set(legend_h, 'units', 'normalized');
set(gca, 'units', 'normalized');
end