1 | function [TD, varargout] = twissring(RING,DP,varargin) |
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2 | %TWISSRING calculates linear optics functions for an UNCOUPLED ring |
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3 | % |
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4 | % [TwissData, tune] = TWISSRING(LATTICE,DP) calculates twiss parameters |
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5 | % and closed orbit coordinates at the RING entrance assuming |
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6 | % constant energy deviation DP. |
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7 | % |
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8 | % [TwissData, tune] = TWISSRING(LATTICE,DP,REFPTS) calculates Twiss parameters |
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9 | % and closed orbit coordinates at specified reference points REFPTS. |
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10 | % |
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11 | % Note: REFPTS is an array of increasing indexes that |
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12 | % select elements from range 1 to length(LATTICE)+1. |
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13 | % See further explanation of REFPTS in the 'help' for FINDSPOS |
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14 | % |
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15 | % [TwissData, tune, chrom] = TWISSRING(...,'chrom', DDP) also calculates |
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16 | % linear dispersion and chromaticity. Dispersion is returned as one |
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17 | % of the fields in TwissData. |
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18 | % !!! Last argument DDP is a momentum deviation on top |
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19 | % of DP (the second argument) used to calculate and normalize |
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20 | % dispersion and chromaticity. If not supplied |
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21 | % the default value of 1e-8 is used. |
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22 | % |
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23 | % Note: To resolve the integer part of the tune |
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24 | % and the uncertainty of acos(trace(M)/2) it is necessary to |
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25 | % supply sufficient number of REFPTS properly spaced in betatron phase. |
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26 | % |
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27 | % TwisData is a 1-by-REFPTS (1-by-1) structure array with fields |
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28 | % (Some are the same as in the output of LINOPT) |
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29 | % ElemIndex - integer (element number) in the RING |
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30 | % SPos - longitudinal position [m] |
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31 | % ClosedOrbit - closed orbit column vector with |
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32 | % components x, px, y, py (momentums, NOT angles) |
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33 | % Dispersion - dispersion orbit position 4-by-1 vector with |
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34 | % components [eta_x, eta_prime_x, eta_y, eta_prime_y]' |
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35 | % calculated with respect to the closed orbit with |
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36 | % momentum deviation DP |
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37 | % M44 - 4x4 transfer matrix M from the beginning of RING |
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38 | % to the entrance of the element for specified DP [2] |
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39 | % beta - [betax, betay] horizontal and vertical Twiss parameter beta |
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40 | % alpha - [alphax, alphay] horizontal and vertical Twiss parameter alpha |
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41 | % mu - [mux, muy] horizontal and vertical betatron phase |
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42 | % !!! NOT 2*PI normalized |
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43 | % |
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44 | % Use MATLAB function CAT to get the data from fields of TwissData into MATLAB arrays. |
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45 | % Example: |
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46 | % >> TD = twissring(THERING,0,1:length(THERING)); |
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47 | % >> BETA = cat(1,TD.beta); |
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48 | % >> S = cat(1,TD.SPos); |
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49 | % >> plot(S,BETA(:,1)) |
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50 | % |
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51 | % See also TWISSLINE, LINOPT, TUNECHROM. |
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52 | |
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53 | NE=length(RING); |
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54 | DDP_default = 1e-8; |
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55 | % Process input arguments |
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56 | switch nargin |
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57 | case 2 |
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58 | REFPTS=NE+1; |
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59 | CHROMFLAG=0; |
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60 | case 3 |
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61 | if isnumeric(varargin{1}) |
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62 | REFPTS = varargin{1}; |
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63 | CHROMFLAG = 0; |
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64 | elseif ischar(varargin{1}) & strncmp(lower(varargin{1}),'chrom',5) |
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65 | CHROMFLAG = 1; |
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66 | REFPTS = NE+1; |
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67 | DDP = DDP_default; |
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68 | else |
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69 | error('Third argument must be a numeric array or string'); |
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70 | end |
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71 | case 4 |
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72 | if isnumeric(varargin{1}) |
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73 | REFPTS = varargin{1}; |
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74 | if ischar(varargin{2}) & strncmp(lower(varargin{2}),'chrom',5) |
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75 | CHROMFLAG = 1; |
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76 | DDP = DDP_default; |
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77 | else |
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78 | error('Fourth argument - wrong type'); |
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79 | end |
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80 | elseif ischar(varargin{1}) & strncmp(lower(varargin{1}),'chrom',5) |
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81 | CHROMFLAG = 1; |
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82 | REFPTS = NE+1; |
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83 | if isnumeric(varargin{2}) |
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84 | DDP = varargin{2}; |
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85 | else |
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86 | error('Fourth argument - wrong type'); |
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87 | end |
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88 | end |
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89 | case 5 |
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90 | if isnumeric(varargin{1}) |
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91 | REFPTS = varargin{1}; |
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92 | else |
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93 | error('Third argument - wrong type'); |
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94 | end |
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95 | if ischar(varargin{2}) & strncmp(lower(varargin{2}),'chrom',5) |
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96 | CHROMFLAG = 1; |
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97 | else |
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98 | error('Fourth argument - wrong type'); |
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99 | end |
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100 | if isnumeric(varargin{3}) |
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101 | DDP = varargin{3}; |
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102 | else |
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103 | error('Fifth argument - wrong type'); |
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104 | end |
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105 | otherwise |
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106 | error('Wrong number of arguments'); |
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107 | end |
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108 | |
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109 | % Include the endpoint if it is not already in REFPTS |
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110 | if REFPTS(end)==NE+1 |
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111 | [M44, MS, orb] = findm44(RING,DP,REFPTS); |
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112 | else |
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113 | [M44, MS, orb] = findm44(RING,DP,[REFPTS,NE+1]); |
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114 | end |
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115 | |
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116 | |
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117 | |
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118 | |
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119 | cos_mu_x = (M44(1,1)+M44(2,2))/2; |
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120 | cos_mu_y = (M44(3,3)+M44(4,4))/2; |
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121 | |
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122 | sin_mu_x = sign(M44(1,2))*sqrt(-M44(1,2)*M44(2,1)-(M44(1,1)-M44(2,2))^2/4); |
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123 | sin_mu_y = sign(M44(3,4))*sqrt(-M44(3,4)*M44(4,3)-(M44(3,3)-M44(4,4))^2/4); |
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124 | |
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125 | |
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126 | ax = (M44(1,1)-M44(2,2))/2/sin_mu_x; |
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127 | ay = (M44(3,3)-M44(4,4))/2/sin_mu_y; |
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128 | |
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129 | bx = M44(1,2)/sin_mu_x; |
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130 | by = M44(3,4)/sin_mu_y; |
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131 | |
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132 | BX = squeeze((MS(1,1,:)*bx-MS(1,2,:)*ax).^2 + MS(1,2,:).^2)/bx; |
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133 | BY = squeeze((MS(3,3,:)*by-MS(3,4,:)*ay).^2 + MS(3,4,:).^2)/by; |
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134 | |
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135 | |
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136 | AX = -squeeze((MS(1,1,:)*bx-MS(1,2,:)*ax).*(MS(2,1,:)*bx-MS(2,2,:)*ax) + MS(1,2,:).*MS(2,2,:))/bx; |
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137 | AY = -squeeze((MS(3,3,:)*by-MS(3,4,:)*ay).*(MS(4,3,:)*by-MS(4,4,:)*ay) + MS(3,4,:).*MS(4,4,:))/by; |
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138 | |
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139 | MX = atan(squeeze( MS(1,2,:)./(MS(1,1,:)*bx-MS(1,2,:)*ax))); |
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140 | MY = atan(squeeze(MS(3,4,:)./(MS(3,3,:)*by-MS(3,4,:)*ay))); |
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141 | |
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142 | MX = BetatronPhaseUnwrap(MX); |
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143 | MY = BetatronPhaseUnwrap(MY); |
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144 | |
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145 | tune = [MX(end),MY(end)]/2/pi; |
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146 | |
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147 | NR = length(REFPTS); |
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148 | % Build TD only for points originally referenced in REFPTS |
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149 | TD = struct('ElemIndex',num2cell(REFPTS),... |
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150 | 'SPos',num2cell(findspos(RING,REFPTS)),... |
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151 | 'ClosedOrbit',num2cell(orb(:,1:NR),1),... |
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152 | 'M44', squeeze(num2cell(MS(:,:,1:NR),[1 2]))',... |
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153 | 'beta', num2cell([BX(1:NR),BY(1:NR)],2)',... |
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154 | 'alpha', num2cell([AX(1:NR),AY(1:NR)],2)',... |
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155 | 'mu', num2cell([MX(1:NR),MY(1:NR)],2)'); |
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156 | |
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157 | |
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158 | if CHROMFLAG |
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159 | [TD_DDP tune_DDP] = twissring(RING,DP+DDP,REFPTS); |
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160 | DORBIT = reshape(cat(1,TD_DDP.ClosedOrbit),4,[]); |
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161 | DISPERSION = num2cell((DORBIT-orb(:,1:NR))/DDP,1); |
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162 | [TD.Dispersion] = deal( DISPERSION{:}); |
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163 | end |
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164 | |
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165 | if nargout>1 |
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166 | varargout{1}=tune; |
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167 | end |
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168 | if nargout==3 & CHROMFLAG |
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169 | varargout{2} = (tune_DDP-tune)/DDP; |
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170 | end |
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171 | |
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172 | function UP = BetatronPhaseUnwrap(P) |
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173 | % unwrap negative jumps in betatron |
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174 | DP = diff(P); |
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175 | JUMPS = [0; diff(P)] < 0; |
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176 | UP = P+cumsum(JUMPS)*pi; |
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177 | |
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178 | |
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