Problem:The beam port - Revision history

https://e-learning.pan-training.eu/wiki/index.php?action=history&feed=atom&title=Problem%3AThe_beam_port Problem:The beam port - Revision history 2026-04-22T01:33:50Z Revision history for this page on the wiki MediaWiki 1.39.1 https://e-learning.pan-training.eu/wiki/index.php?title=Problem:The_beam_port&diff=1403&oldid=prev Wikiadmin: Wikiadmin moved page Problem: The beam port to Problem:The beam port 2020-09-20T15:26:42Z

<p>Wikiadmin moved page <a href="/wiki/Problem:_The_beam_port" class="mw-redirect" title="Problem: The beam port">Problem: The beam port</a> to <a href="/wiki/Problem:The_beam_port" title="Problem:The beam port">Problem:The beam port</a></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <tr class="diff-title" lang="en"> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:26, 20 September 2020</td> </tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div> </td></tr></table>

Wikiadmin https://e-learning.pan-training.eu/wiki/index.php?title=Problem:The_beam_port&diff=1363&oldid=prev Wikiadmin: /* Question 2 */ 2020-04-20T13:03:58Z

<p><span dir="auto"><span class="autocomment">Question 2</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:03, 20 April 2020</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l39">Line 39:</td> <td colspan="2" class="diff-lineno">Line 39:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{hidden begin|toggle=right|title=Solution|titlestyle=background:#ccccff}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{hidden begin|toggle=right|title=Solution|titlestyle=background:#ccccff}}</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><figure id="fig:Beamport">[[Image:<del style="font-weight: bold; text-decoration: none;">Beamport</del>.jpg | thumb | 400px | <caption>Schematical sideview of a source and beam. The position in case A is underilluminated (not shielded by the beamport), whereas case B is shielded by the beamport. The moderator (source) has area \( \int dA_m = A_m = d_m^2\).</caption>]]</figure></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><figure id="fig:Beamport">[[Image:<ins style="font-weight: bold; text-decoration: none;">Beamport1</ins>.jpg | thumb | 400px | <caption>Schematical sideview of a source and beam. The position in case A is underilluminated (not shielded by the beamport), whereas case B is shielded by the beamport. The moderator (source) has area \( \int dA_m = A_m = d_m^2\).</caption>]]</figure></div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><figure id="fig:Flux_beamport">[[Image:<del style="font-weight: bold; text-decoration: none;">Flux_beamport</del>.png | thumb | 400px | <caption>The flux \(\Psi\)[cts/(s\(\cdot\)cm\(^2\))] through a small area at position L normalised to a source flux of \(\Psi_0\)= 1 [cts/(s\(\cdot\)str)].</caption>]]</figure></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><figure id="fig:Flux_beamport">[[Image:<ins style="font-weight: bold; text-decoration: none;">Flux_beamport1</ins>.png | thumb | 400px | <caption>The flux \(\Psi\)[cts/(s\(\cdot\)cm\(^2\))] through a small area at position L normalised to a source flux of \(\Psi_0\)= 1 [cts/(s\(\cdot\)str)].</caption>]]</figure></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the following the width and height of the square moderator is denoted \(d_m\) and the width and height of the square beamport denoted \(d_p\). For \(L<L'\) (case A, underilluminated beam port), the moderator is not shielded by the beamport, but for \(L>L'\) (case B) the moderator is shielded by the beamport, see <xr id="fig:Beamport">Figure %i</xr>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the following the width and height of the square moderator is denoted \(d_m\) and the width and height of the square beamport denoted \(d_p\). For \(L<L'\) (case A, underilluminated beam port), the moderator is not shielded by the beamport, but for \(L>L'\) (case B) the moderator is shielded by the beamport, see <xr id="fig:Beamport">Figure %i</xr>.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In general, the integrated intensity radiated in \(d\Omega\) from a source with area \(A_m\) is</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In general, the integrated intensity radiated in \(d\Omega\) from a source with area \(A_m\) is</div></td></tr> </table>

Wikiadmin https://e-learning.pan-training.eu/wiki/index.php?title=Problem:The_beam_port&diff=1037&oldid=prev Wikiadmin: 1 revision imported 2020-02-18T22:15:12Z

<p>1 revision imported</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <tr class="diff-title" lang="en"> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:15, 18 February 2020</td> </tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div> </td></tr></table>

Wikiadmin https://e-learning.pan-training.eu/wiki/index.php?title=Problem:The_beam_port&diff=1036&oldid=prev ucph>Tommy: Created page with "  <!-- Consider a moderator of a typ..." 2019-07-14T21:26:45Z

<p>Created page with "  <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> We define the intensity from a point source emitted in the solid angle \(d\Omega\) by \(I=\int d\Omega \Psi\).<br /> <br /> =====Question 1=====<br /> Consider first a point source which emits flux \(\Psi_0\) [cts/(s\(\cdot\)ster)]. Calculate the intensity at position \(L\) downstream from the source through a small area \(\Delta A\) (''e.g.'' of a detector). <br /> <br /> {{hidden begin|toggle=right|title=Solution|titlestyle=background:#ccccff}}<br /> The intensity will be given by<br /> <br /> :\( I=\displaystyle\int d\Omega \, \Psi_0 = \displaystyle\int_{\Delta A} dA \, \dfrac{\Psi_0}{L^2} \approx \dfrac{\Psi_0}{L^2} \Delta A \) <br /> {{hidden end }}<br /> <br /> =====Question 2=====<br /> Consider now a moderator of a typical useful size of \(150\times 150\) mm\(^2\). The moderator emits neutrons isotropically and uniformly over its surface with "source flux" \(\Psi_0\) [cts/(s\(\cdot\)m\(^2 \cdot\)ster)]. A beam port (slit) of size \(50\times50\) mm\(^2\) is placed 4 m from the moderator face. Consider a small area \(d A\) centered at the moderator-beam port axis; downstream from the beam port. Calculate how the neutron flux through \(d A\) varies with distance, \(L\), from the moderator.<br /> <br /> {{hidden begin|toggle=right|title=Hint|titlestyle=background:#ccccff}}<br /> The variation in distance between any point of the moderator and any point of the beam port can safely be ignored. Gravity can be neglected.<br /> {{hidden end}} <br /> {{hidden begin|toggle=right|title=Hint|titlestyle=background:#ccccff}}<br /> At a certain position (\(L'\)) of \(d A\), the beamport it starts to block part of the view to the moderator.<br /> {{hidden end}} <br /> <br /> {{hidden begin|toggle=right|title=Solution|titlestyle=background:#ccccff}}<br /> <figure id="fig:Beamport">[[Image:Beamport.jpg | thumb | 400px | <caption>Schematical sideview of a source and beam. The position in case A is underilluminated (not shielded by the beamport), whereas case B is shielded by the beamport. The moderator (source) has area \( \int dA_m = A_m = d_m^2\).</caption>]]</figure><br /> <figure id="fig:Flux_beamport">[[Image:Flux_beamport.png | thumb | 400px | <caption>The flux \(\Psi\)[cts/(s\(\cdot\)cm\(^2\))] through a small area at position L normalised to a source flux of \(\Psi_0\)= 1 [cts/(s\(\cdot\)str)].</caption>]]</figure><br /> In the following the width and height of the square moderator is denoted \(d_m\) and the width and height of the square beamport denoted \(d_p\). For \(L<L'\) (case A, underilluminated beam port), the moderator is not shielded by the beamport, but for \(L>L'\) (case B) the moderator is shielded by the beamport, see <xr id="fig:Beamport">Figure %i</xr>.<br /> In general, the integrated intensity radiated in \(d\Omega\) from a source with area \(A_m\) is<br /> <br /> :\( \mathcal{I} = \displaystyle\int dA_m \, I = \displaystyle\int dA_m \displaystyle\int d\Omega \, \Psi_0 = \displaystyle\int dA_m \displaystyle\int dA \, \dfrac{\Psi_0}{L^2} \approx A_m\, \Delta A\, \dfrac{\Psi_0}{L^2} ,\)<br /> <br /> where variations in the distance from different places on the source to the point \(L\) has been neglected. The flux is then<br /> <br /> :\( \Psi = \dfrac{\mathcal{I}}{\Delta A} = A_m\, \dfrac{\Psi_0}{L^2} .\)<br /> <br /> Inserting a beamport does not change the flux for \(L<L'\) ,<br /> <br /> :\( \Psi_{L<L'} = A_m \dfrac{\Psi_0}{L^2} = d_m^2 \dfrac{\Psi_0}{L^2} = 0.0225 \dfrac{\Psi_0}{L^2}, \)<br /> <br /> where \(L\) is the distance from the source (moderator) with area. <br /> <br /> The flux at \(L\geq L'\) is<br /> <br /> :\( \begin{align*} <br /> \Psi_{L>L'} &= A_m^{\text{eff}} \dfrac{\Psi_0}{L^2} \\<br /> &= (d_m^{\text{eff}})^2 \dfrac{\Psi_0}{L^2} \\<br /> &= d_p^2 \left(\dfrac{L}{L-L_{\text{port}}}\right)^2 \dfrac{\Psi_0}{L^2} \\<br /> &= d_p^2 \dfrac{\Psi_0}{(L-L_{\text{port}})^2} \\<br /> &= 0.0025 \dfrac{\Psi_0}{(L-4)^2}, <br /> \end{align*}\)<br /> <br /> since the beamport 'shields' the moderator giving an effective source size of \((d^{\text{eff}})^2\). ''I.e.'' effectively the detector (\(\Delta A\)) sees a virtual source of size \((d_m^{\text{eff}})^2\) at distance \(L-L_{\text{port}}\). The flux is plotted in <xr id="fig:Flux_beamport">Figure %i</xr>.<br /> {{hidden end}}<br /> <br /> =====Question 3=====<br /> The divergence, \(\eta\), of a neutron is defined as the angular deviation of the neutron velocity to the main axis. Calculate the maximal divergence as a function of \(L\) for the cases described above.<br /> <br /> {{hidden begin|toggle=right|title=Solution|titlestyle=background:#ccccff}}<br /> The maximum divergence in the the underilluminated case where \(L<L'\) is<br /> <br /> :\( \eta_{L<L'} = \tan^{-1}\dfrac{d_m}{2L} .\)<br /> <br /> Similarly, the maximum divergence in the case where \(L\geq L'\) is<br /> <br /> :\( \eta_{L\geq L'} = \tan^{-1}\dfrac{d_p}{2(L-L_{\text{port}})} .\)<br /> {{hidden end}}</div>

ucph>Tommy