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<div id="projectbrief">Simulate particle behavior inside a Penning Trap</div>
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<a href="main_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include &lt;complex&gt;</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#include &lt;fstream&gt;</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include &lt;omp.h&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include &lt;string&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include &quot;<a class="code" href="PenningTrap_8hpp.html">PenningTrap.hpp</a>&quot;</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include &quot;<a class="code" href="utils_8hpp.html">utils.hpp</a>&quot;</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#define PARTICLES 100</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#define N 40000</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#define CHARGE 1. </span><span class="comment">// unit: e</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#define MASS 40. </span><span class="comment">// unit: amu</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> </div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">// Particles used for testing</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"><a class="line" href="main_8cpp.html#a87da4ef9f2cd753579484824310467b8"> 29</a></span><a class="code hl_class" href="classParticle.html">Particle</a> <a class="code hl_variable" href="main_8cpp.html#a87da4ef9f2cd753579484824310467b8">p1</a>(CHARGE, MASS, <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>{20., 0., 20.}, <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>{0., 25., 0.}); </div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"><a class="line" href="main_8cpp.html#a90f661586eb3c318fdca6f95ebc4fc46"> 30</a></span><a class="code hl_class" href="classParticle.html">Particle</a> <a class="code hl_variable" href="main_8cpp.html#a90f661586eb3c318fdca6f95ebc4fc46">p2</a>(CHARGE, MASS, <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>{25., 25., 0.}, <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>{0., 40., 5.}); </div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"><a class="line" href="main_8cpp.html#a6451833d72816ef393087956c766125b"> 38</a></span><a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="main_8cpp.html#a6451833d72816ef393087956c766125b">analytical_solution_particle_1</a>(<span class="keywordtype">double</span> t)</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span>{</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordtype">double</span> w_0 = <a class="code hl_define" href="constants_8hpp.html#a0acb682b8260ab1c60b918599864e2e5">T</a> / MASS;</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keywordtype">double</span> w_z2 = (50. * <a class="code hl_define" href="constants_8hpp.html#af40a326b23c68a27cebe60f16634a2cb">V</a> / 1000.) / (MASS * 500. * 500.);</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordtype">double</span> w_p = (w_0 + std::sqrt(w_0 * w_0 - 2. * w_z2)) / 2.;</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordtype">double</span> w_n = (w_0 - std::sqrt(w_0 * w_0 - 2. * w_z2)) / 2.;</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordtype">double</span> A_p = (25. + w_n * 20.) / (w_n - w_p);</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordtype">double</span> A_n = -(25. + w_p * 20.) / (w_n - w_p);</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> std::complex&lt;double&gt; f =</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> A_p * std::exp(std::complex&lt;double&gt;(0., -w_p * t)) +</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> A_n * std::exp(std::complex&lt;double&gt;(0., -w_n * t));</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> res{std::real(f), std::imag(f), 20. * std::cos(std::sqrt(w_z2) * t)};</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordflow">return</span> res;</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span>}</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> </div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"><a class="line" href="main_8cpp.html#a8fdbe2d5a872e50ef5ec1263243589d6"> 55</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="main_8cpp.html#a8fdbe2d5a872e50ef5ec1263243589d6">simulate_single_particle</a>()</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span>{</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// Initialize trap with particle 1</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap(std::vector&lt;Particle&gt;{<a class="code hl_variable" href="main_8cpp.html#a87da4ef9f2cd753579484824310467b8">p1</a>});</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordtype">double</span> time = 50.; <span class="comment">// microseconds</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> </div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// Simulate and write results to file</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> trap.<a class="code hl_function" href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">write_simulation_to_dir</a>(<span class="stringliteral">&quot;output/simulate_single_particle&quot;</span>, time, N,</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="stringliteral">&quot;rk4&quot;</span>, <span class="keyword">false</span>);</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span>}</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> </div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"><a class="line" href="main_8cpp.html#a783789519f97c6430081171cacb0ffb1"> 70</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="main_8cpp.html#a783789519f97c6430081171cacb0ffb1">simulate_two_particles</a>()</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span>{</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="comment">// Initialize traps with particles</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap_no_interaction(std::vector&lt;Particle&gt;{<a class="code hl_variable" href="main_8cpp.html#a87da4ef9f2cd753579484824310467b8">p1</a>, <a class="code hl_variable" href="main_8cpp.html#a90f661586eb3c318fdca6f95ebc4fc46">p2</a>});</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap_with_interaction(std::vector&lt;Particle&gt;{<a class="code hl_variable" href="main_8cpp.html#a87da4ef9f2cd753579484824310467b8">p1</a>, <a class="code hl_variable" href="main_8cpp.html#a90f661586eb3c318fdca6f95ebc4fc46">p2</a>});</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> </div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordtype">double</span> time = 50.; <span class="comment">// microseconds</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> </div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// Simulate and write results to files</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> trap_no_interaction.<a class="code hl_function" href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">write_simulation_to_dir</a>(</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="stringliteral">&quot;output/simulate_2_particles/no_interaction&quot;</span>, time, N, <span class="stringliteral">&quot;rk4&quot;</span>, <span class="keyword">false</span>);</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> trap_with_interaction.write_simulation_to_dir(</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="stringliteral">&quot;output/simulate_2_particles/with_interaction&quot;</span>, time, N);</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span>}</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"><a class="line" href="main_8cpp.html#ac67e0d59227856c4d42e7d01c75e0ad2"> 88</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="main_8cpp.html#ac67e0d59227856c4d42e7d01c75e0ad2">simulate_single_particle_with_different_steps</a>()</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span>{</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordtype">double</span> time = 50.; <span class="comment">// microseconds</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> std::ofstream ofile;</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> </div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="comment">// Calculate relative error for RK4</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> std::string path = <span class="stringliteral">&quot;output/relative_error/RK4/&quot;</span>;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <a class="code hl_function" href="utils_8hpp.html#a6fdd7217b750aff5b6295ece7cbdeffa">mkpath</a>(path);</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 4; i++) {</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordtype">int</span> steps = 4000 * std::pow(2, i);</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keywordtype">double</span> dt = time / (double)steps;</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> ofile.open(path + std::to_string(steps) + <span class="stringliteral">&quot;_steps.txt&quot;</span>);</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap(std::vector&lt;Particle&gt;{<a class="code hl_variable" href="main_8cpp.html#a87da4ef9f2cd753579484824310467b8">p1</a>});</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <a class="code hl_struct" href="structsimulation.html">simulation_t</a> res = trap.simulate(time, steps, <span class="stringliteral">&quot;rk4&quot;</span>, <span class="keyword">false</span>);</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; steps; i++) {</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> ofile &lt;&lt; arma::norm(res.r_vecs[0][i] -</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <a class="code hl_function" href="main_8cpp.html#a6451833d72816ef393087956c766125b">analytical_solution_particle_1</a>(dt*i))</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> }</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> ofile.close();</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> }</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> </div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="comment">// Calculate relative error for forward Euler</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> path = <span class="stringliteral">&quot;output/relative_error/euler/&quot;</span>;</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <a class="code hl_function" href="utils_8hpp.html#a6fdd7217b750aff5b6295ece7cbdeffa">mkpath</a>(path);</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 4; i++) {</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keywordtype">int</span> steps = 4000 * std::pow(2, i);</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="keywordtype">double</span> dt = time / (double)steps;</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> ofile.open(path + std::to_string(steps) + <span class="stringliteral">&quot;_steps.txt&quot;</span>);</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap(std::vector&lt;Particle&gt;{<a class="code hl_variable" href="main_8cpp.html#a87da4ef9f2cd753579484824310467b8">p1</a>});</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <a class="code hl_struct" href="structsimulation.html">simulation_t</a> res = trap.simulate(time, steps, <span class="stringliteral">&quot;euler&quot;</span>, <span class="keyword">false</span>);</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; steps; i++) {</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> ofile &lt;&lt; arma::norm(res.r_vecs[0][i] -</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <a class="code hl_function" href="main_8cpp.html#a6451833d72816ef393087956c766125b">analytical_solution_particle_1</a>(dt*i))</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> }</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> ofile.close();</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> }</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span>}</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> </div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"><a class="line" href="main_8cpp.html#a213713d6ecc02a32b588ffd179dc7513"> 131</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="main_8cpp.html#a213713d6ecc02a32b588ffd179dc7513">simulate_100_particles</a>()</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span>{</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap((<span class="keywordtype">unsigned</span>)100);</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> </div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="keywordtype">double</span> time = 50.; <span class="comment">// microseconds</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> </div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> trap.<a class="code hl_function" href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">write_simulation_to_dir</a>(<span class="stringliteral">&quot;output/simulate_100_particles&quot;</span>, time, N);</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span>}</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> </div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"><a class="line" href="main_8cpp.html#a330668384dc073980ba11116309bacc5"> 146</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="main_8cpp.html#a330668384dc073980ba11116309bacc5">simulate_100_particles_with_time_potential</a>()</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span>{</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="keywordtype">double</span> time = 500.;</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> </div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keywordtype">double</span> amplitudes[]{.1, .4, .7};</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> </div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keywordtype">double</span> freq_start = .2;</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <span class="keywordtype">double</span> freq_end = 2.5;</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="keywordtype">double</span> freq_increment = .02;</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="keywordtype">size_t</span> freq_iterations = (size_t)((freq_end - freq_start) / freq_increment);</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> </div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keywordtype">double</span> res[4][freq_iterations];</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> </div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> std::string path = <span class="stringliteral">&quot;output/time_dependent_potential/&quot;</span>;</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <a class="code hl_function" href="utils_8hpp.html#a6fdd7217b750aff5b6295ece7cbdeffa">mkpath</a>(path);</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> </div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> std::ofstream ofile;</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> </div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <span class="keywordtype">double</span> freq = freq_start;</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; freq_iterations; i++) {</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> res[0][i] = freq;</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> freq += freq_increment;</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> }</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> </div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span><span class="preprocessor">#pragma omp parallel for collapse(2) num_threads(4)</span></div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; 3; i++) {</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; freq_iterations; j++) {</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap(</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> (<span class="keywordtype">unsigned</span>)100, <a class="code hl_define" href="constants_8hpp.html#a0acb682b8260ab1c60b918599864e2e5">T</a>,</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> std::bind(</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> [](<span class="keywordtype">double</span> f, <span class="keywordtype">double</span> r, <span class="keywordtype">double</span> t) {</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="keywordflow">return</span> (25. * <a class="code hl_define" href="constants_8hpp.html#af40a326b23c68a27cebe60f16634a2cb">V</a> / 1000.) * (1. + f * std::cos(r * t));</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> },</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> amplitudes[i], res[0][j], std::placeholders::_1),</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> 500., 0.);</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> res[i + 1][j] =</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> trap.<a class="code hl_function" href="classPenningTrap.html#a0194be61c956a9259c747c23e4163c5b">fraction_of_particles_left</a>(time, N, <span class="stringliteral">&quot;rk4&quot;</span>, <span class="keyword">false</span>);</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> }</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> }</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> </div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> ofile.open(path + <span class="stringliteral">&quot;res.txt&quot;</span>);</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; freq_iterations; i++) {</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> ofile &lt;&lt; res[0][i] &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; res[1][i] &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; res[2][i] &lt;&lt; <span class="stringliteral">&quot;,&quot;</span></div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> &lt;&lt; res[3][i] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> }</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> ofile.close();</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span>}</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> </div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span><span class="keywordtype">int</span> main()</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span>{</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <span class="keywordtype">double</span> t0 = omp_get_wtime();</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> </div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="comment">// simulate_single_particle();</span></div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> </div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="comment">// simulate_two_particles();</span></div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> </div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> <a class="code hl_function" href="main_8cpp.html#ac67e0d59227856c4d42e7d01c75e0ad2">simulate_single_particle_with_different_steps</a>();</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> </div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <span class="keywordtype">double</span> t1 = omp_get_wtime();</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> </div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> <a class="code hl_function" href="main_8cpp.html#a213713d6ecc02a32b588ffd179dc7513">simulate_100_particles</a>();</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> </div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="comment">//simulate_100_particles_with_time_potential();</span></div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> </div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="keywordtype">double</span> end = omp_get_wtime();</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> </div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Time: &quot;</span> &lt;&lt; (end - t1) &lt;&lt; <span class="stringliteral">&quot; seconds&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> </div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span>}</div>
<div class="ttc" id="aPenningTrap_8hpp_html"><div class="ttname"><a href="PenningTrap_8hpp.html">PenningTrap.hpp</a></div><div class="ttdoc">A class for simulating a Penning trap.</div></div>
<div class="ttc" id="aclassParticle_html"><div class="ttname"><a href="classParticle.html">Particle</a></div><div class="ttdoc">A class that holds attributes of a particle.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00021">Particle.hpp:21</a></div></div>
<div class="ttc" id="aclassPenningTrap_html"><div class="ttname"><a href="classPenningTrap.html">PenningTrap</a></div><div class="ttdoc">A class that simulates a Penning trap.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00031">PenningTrap.hpp:31</a></div></div>
<div class="ttc" id="aclassPenningTrap_html_a0194be61c956a9259c747c23e4163c5b"><div class="ttname"><a href="classPenningTrap.html#a0194be61c956a9259c747c23e4163c5b">PenningTrap::fraction_of_particles_left</a></div><div class="ttdeci">double fraction_of_particles_left(double time, unsigned int steps, std::string method=&quot;rk4&quot;, bool particle_interaction=true)</div><div class="ttdoc">Simulate and calculate what fraction of particles are still left inside the Penning trap after the si...</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00281">PenningTrap.cpp:281</a></div></div>
<div class="ttc" id="aclassPenningTrap_html_abbb832a85139b1a56ebde57d7b8f9a57"><div class="ttname"><a href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">PenningTrap::write_simulation_to_dir</a></div><div class="ttdeci">void write_simulation_to_dir(std::string path, double time, unsigned int steps, std::string method=&quot;rk4&quot;, bool particle_interaction=true)</div><div class="ttdoc">Simulate and write the displacement of all particles to files.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00246">PenningTrap.cpp:246</a></div></div>
<div class="ttc" id="aconstants_8hpp_html_a0acb682b8260ab1c60b918599864e2e5"><div class="ttname"><a href="constants_8hpp.html#a0acb682b8260ab1c60b918599864e2e5">T</a></div><div class="ttdeci">#define T</div><div class="ttdoc">1 Tesla. unit:</div><div class="ttdef"><b>Definition:</b> <a href="constants_8hpp_source.html#l00017">constants.hpp:17</a></div></div>
<div class="ttc" id="aconstants_8hpp_html_af40a326b23c68a27cebe60f16634a2cb"><div class="ttname"><a href="constants_8hpp.html#af40a326b23c68a27cebe60f16634a2cb">V</a></div><div class="ttdeci">#define V</div><div class="ttdoc">1 Volt. unit:</div><div class="ttdef"><b>Definition:</b> <a href="constants_8hpp_source.html#l00019">constants.hpp:19</a></div></div>
<div class="ttc" id="amain_8cpp_html_a213713d6ecc02a32b588ffd179dc7513"><div class="ttname"><a href="main_8cpp.html#a213713d6ecc02a32b588ffd179dc7513">simulate_100_particles</a></div><div class="ttdeci">void simulate_100_particles()</div><div class="ttdoc">Simulate 100 particles over 50 .</div><div class="ttdef"><b>Definition:</b> <a href="main_8cpp_source.html#l00131">main.cpp:131</a></div></div>
<div class="ttc" id="amain_8cpp_html_a330668384dc073980ba11116309bacc5"><div class="ttname"><a href="main_8cpp.html#a330668384dc073980ba11116309bacc5">simulate_100_particles_with_time_potential</a></div><div class="ttdeci">void simulate_100_particles_with_time_potential()</div><div class="ttdoc">Simulate 100 particles over 500 using a time dependent potential.</div><div class="ttdef"><b>Definition:</b> <a href="main_8cpp_source.html#l00146">main.cpp:146</a></div></div>
<div class="ttc" id="amain_8cpp_html_a6451833d72816ef393087956c766125b"><div class="ttname"><a href="main_8cpp.html#a6451833d72816ef393087956c766125b">analytical_solution_particle_1</a></div><div class="ttdeci">vec_3d analytical_solution_particle_1(double t)</div><div class="ttdoc">The analytical solution for particle p1.</div><div class="ttdef"><b>Definition:</b> <a href="main_8cpp_source.html#l00038">main.cpp:38</a></div></div>
<div class="ttc" id="amain_8cpp_html_a783789519f97c6430081171cacb0ffb1"><div class="ttname"><a href="main_8cpp.html#a783789519f97c6430081171cacb0ffb1">simulate_two_particles</a></div><div class="ttdeci">void simulate_two_particles()</div><div class="ttdoc">Simulate 2 particles over the period of 50 with and without particle interactions.</div><div class="ttdef"><b>Definition:</b> <a href="main_8cpp_source.html#l00070">main.cpp:70</a></div></div>
<div class="ttc" id="amain_8cpp_html_a87da4ef9f2cd753579484824310467b8"><div class="ttname"><a href="main_8cpp.html#a87da4ef9f2cd753579484824310467b8">p1</a></div><div class="ttdeci">Particle p1(CHARGE, MASS, vec_3d{20., 0., 20.}, vec_3d{0., 25., 0.})</div><div class="ttdoc">Particle 1.</div></div>
<div class="ttc" id="amain_8cpp_html_a8fdbe2d5a872e50ef5ec1263243589d6"><div class="ttname"><a href="main_8cpp.html#a8fdbe2d5a872e50ef5ec1263243589d6">simulate_single_particle</a></div><div class="ttdeci">void simulate_single_particle()</div><div class="ttdoc">Simulate a single particle over the period of 50 .</div><div class="ttdef"><b>Definition:</b> <a href="main_8cpp_source.html#l00055">main.cpp:55</a></div></div>
<div class="ttc" id="amain_8cpp_html_a90f661586eb3c318fdca6f95ebc4fc46"><div class="ttname"><a href="main_8cpp.html#a90f661586eb3c318fdca6f95ebc4fc46">p2</a></div><div class="ttdeci">Particle p2(CHARGE, MASS, vec_3d{25., 25., 0.}, vec_3d{0., 40., 5.})</div><div class="ttdoc">Particle 2.</div></div>
<div class="ttc" id="amain_8cpp_html_ac67e0d59227856c4d42e7d01c75e0ad2"><div class="ttname"><a href="main_8cpp.html#ac67e0d59227856c4d42e7d01c75e0ad2">simulate_single_particle_with_different_steps</a></div><div class="ttdeci">void simulate_single_particle_with_different_steps()</div><div class="ttdoc">Simulate a single particle over 50 using different amount of steps and different methods.</div><div class="ttdef"><b>Definition:</b> <a href="main_8cpp_source.html#l00088">main.cpp:88</a></div></div>
<div class="ttc" id="astructsimulation_html"><div class="ttname"><a href="structsimulation.html">simulation</a></div><div class="ttdoc">Typedef for PenningTrap::simulation return value.</div><div class="ttdef"><b>Definition:</b> <a href="typedefs_8hpp_source.html#l00040">typedefs.hpp:40</a></div></div>
<div class="ttc" id="atypedefs_8hpp_html_a9f33f4962c8fb62cc5ccd0e4e039a8df"><div class="ttname"><a href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a></div><div class="ttdeci">arma::vec::fixed&lt; 3 &gt; vec_3d</div><div class="ttdoc">Typedef for a fixed 3d arma vector.</div><div class="ttdef"><b>Definition:</b> <a href="typedefs_8hpp_source.html#l00036">typedefs.hpp:36</a></div></div>
<div class="ttc" id="autils_8hpp_html"><div class="ttname"><a href="utils_8hpp.html">utils.hpp</a></div><div class="ttdoc">Function prototypes and macros that are useful.</div></div>
<div class="ttc" id="autils_8hpp_html_a6fdd7217b750aff5b6295ece7cbdeffa"><div class="ttname"><a href="utils_8hpp.html#a6fdd7217b750aff5b6295ece7cbdeffa">mkpath</a></div><div class="ttdeci">bool mkpath(std::string path, int mode=0777)</div><div class="ttdoc">Make path given.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00074">utils.cpp:74</a></div></div>
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