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2 changes: 1 addition & 1 deletion previews/PR302/chebyshev/index.html
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v_{j} = \sum_{n=0}^{2N}\frac{J_{n}}{2N+1}\exp\left[-i \frac{2\pi n j}{2N+1}\right].
\end{equation}\]</p><p>Finally, we can compare equations (8) and (15) and deduce that </p><p class="math-container">\[\begin{equation}
w_{j} = q_{j}v_{j} {\rm~for~} 0 \leq j \leq N.
\end{equation}\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../constraints_on_normalized_distribution_function/">Constraints on normalized distribution function »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 11 January 2025 15:27">Saturday 11 January 2025</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
\end{equation}\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../constraints_on_normalized_distribution_function/">Constraints on normalized distribution function »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 11 January 2025 15:31">Saturday 11 January 2025</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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\end{align}\]</p><h3 id="Evolving-n"><a class="docs-heading-anchor" href="#Evolving-n">Evolving <span>$n$</span></a><a id="Evolving-n-1"></a><a class="docs-heading-anchor-permalink" href="#Evolving-n" title="Permalink"></a></h3><p>When evolving only <span>$n$</span> separately, we only need one constraint and the correction is just a re-scaling. This corresponds to <span>$B=0,C=0$</span> so that</p><p class="math-container">\[\begin{align}
1 &amp;= AI_0 \\
A &amp;= \frac{1}{I_0}
\end{align}\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../chebyshev/">« Chebyshev tranform via Fourier transform</a><a class="docs-footer-nextpage" href="../debugging-hints/">Debugging »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 11 January 2025 15:27">Saturday 11 January 2025</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
\end{align}\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../chebyshev/">« Chebyshev tranform via Fourier transform</a><a class="docs-footer-nextpage" href="../debugging-hints/">Debugging »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 11 January 2025 15:31">Saturday 11 January 2025</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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\end{align}\]</p><p>or in 1V simulations</p><p class="math-container">\[\begin{align}
S_i &amp;= A_i(r,z) \left[ \frac{1}{sqrt{\pi} \sqrt{2 T_{\mathrm{source},i} / m_i}} \exp\left( -\frac{v_\perp^2}{T_{\mathrm{source},i}} - f_i(v_\parallel) \right) \right] \\
S_n &amp;= A_n(r,z) \left[ \frac{1}{sqrt{\pi} \sqrt{2 T_{\mathrm{source},n} / m_n}} \exp\left( -\frac{v_z^2}{T_{\mathrm{source},n}} - f_n(v_z) \right) \right]
\end{align}\]</p><p>Note that this source does not give a fixed power input (although that might be a nice feature to have), it just swaps plasma/neutral particles at a constant rate.</p><h2 id="API"><a class="docs-heading-anchor" href="#API">API</a><a id="API-1"></a><a class="docs-heading-anchor-permalink" href="#API" title="Permalink"></a></h2><p>See <a href="../zz_external_sources/#external_sources">external_sources</a>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../developing/">« Developing</a><a class="docs-footer-nextpage" href="../fokker_planck_notes/">Fokker Planck collision operator »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 11 January 2025 15:27">Saturday 11 January 2025</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
\end{align}\]</p><p>Note that this source does not give a fixed power input (although that might be a nice feature to have), it just swaps plasma/neutral particles at a constant rate.</p><h2 id="API"><a class="docs-heading-anchor" href="#API">API</a><a id="API-1"></a><a class="docs-heading-anchor-permalink" href="#API" title="Permalink"></a></h2><p>See <a href="../zz_external_sources/#external_sources">external_sources</a>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../developing/">« Developing</a><a class="docs-footer-nextpage" href="../fokker_planck_notes/">Fokker Planck collision operator »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 11 January 2025 15:31">Saturday 11 January 2025</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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# nuii sets the normalised input C[F,F] Fokker-Planck collision frequency
# for frequency_option = &quot;manual&quot;
nuii = 1.0
frequency_option = &quot;manual&quot;</code></pre><p>Set <code>use_fokker_planck=false</code> to turn off Fokker-Planck collisions without commenting out the namelist. The default option for <code>frequency_option = &quot;reference_parameters&quot;</code>, where <code>nuii</code> is set by the reference parameter inputs. Further specialised input parameters can be seen in the source at <code>setup_fkpl_collisions_input()</code> in <code>moment_kinetics/src/fokker_planck.jl</code>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../external_sources_notes/">« External sources</a><a class="docs-footer-nextpage" href="../geometry/">Magnetic Geometry »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 11 January 2025 15:27">Saturday 11 January 2025</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
frequency_option = &quot;manual&quot;</code></pre><p>Set <code>use_fokker_planck=false</code> to turn off Fokker-Planck collisions without commenting out the namelist. The default option for <code>frequency_option = &quot;reference_parameters&quot;</code>, where <code>nuii</code> is set by the reference parameter inputs. Further specialised input parameters can be seen in the source at <code>setup_fkpl_collisions_input()</code> in <code>moment_kinetics/src/fokker_planck.jl</code>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../external_sources_notes/">« External sources</a><a class="docs-footer-nextpage" href="../geometry/">Magnetic Geometry »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 11 January 2025 15:31">Saturday 11 January 2025</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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= J \frac{E_z B_\zeta}{B^2}.
\end{equation}\]</p><p>Due to the axisymmetry of the system, the differential operator <span>$\mathbf{b} \cdot \nabla (\cdot) = b_z \partial {(\cdot)}{\partial z}$</span>, and the convective derivative</p><p class="math-container">\[\begin{equation}
\frac{d B}{d t} = \frac{d z}{d t} \frac{\partial B}{ \partial z} + \frac{dr}{dt}\frac{\partial B}{\partial r}.
\end{equation}\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../fokker_planck_notes/">« Fokker Planck collision operator</a><a class="docs-footer-nextpage" href="../getting_started/">Getting started »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 11 January 2025 15:27">Saturday 11 January 2025</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
\end{equation}\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../fokker_planck_notes/">« Fokker Planck collision operator</a><a class="docs-footer-nextpage" href="../getting_started/">Getting started »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 11 January 2025 15:31">Saturday 11 January 2025</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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