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Magnetic mirrors / Fermi acceleration - Histórico de revisões
2024-03-29T05:20:15Z
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http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Magnetic_mirrors_/_Fermi_acceleration&diff=3354&oldid=prev
Ist426982 em 15h53min de 17 de junho de 2017
2017-06-17T15:53:47Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 15h53min de 17 de junho de 2017</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l7" >Linha 7:</td>
<td colspan="2" class="diff-lineno">Linha 7:</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>(a) Using the invariance of \(\mu\), find the energy to which the proton is accelerated before it escapes.</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>(a) Using the invariance of \(\mu\), find the energy to which the proton is accelerated before it escapes.</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;"></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;"></td></tr>
<tr><td class='diff-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>(b) How long does it take to reach that energy? Suggestions: i) suppose that the <del class="diffchange diffchange-inline">$</del>B<del class="diffchange diffchange-inline">$ </del>field is approxiamtely uniform in the space between the mirrors and changes abruptly near the mirrors, ''i.e.'', treat each mirror as a flat piston and show that the velocity gained at each bounce is \(2v_m\); ii) compute the number of bounces necessary; iii) assume that the distance between the mirrors does not change appreciably </div></td><td class='diff-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>(b) How long does it take to reach that energy? Suggestions: i) suppose that the <ins class="diffchange diffchange-inline">\(</ins>B<ins class="diffchange diffchange-inline">\) </ins>field is approxiamtely uniform in the space between the mirrors and changes abruptly near the mirrors, ''i.e.'', treat each mirror as a flat piston and show that the velocity gained at each bounce is \(2v_m\); ii) compute the number of bounces necessary; iii) assume that the distance between the mirrors does not change appreciably </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>during the acceleration process.</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>during the acceleration process.</div></td></tr>
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Ist426982
http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Magnetic_mirrors_/_Fermi_acceleration&diff=3352&oldid=prev
Ist426982 em 15h53min de 17 de junho de 2017
2017-06-17T15:53:19Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 15h53min de 17 de junho de 2017</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l7" >Linha 7:</td>
<td colspan="2" class="diff-lineno">Linha 7:</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>(a) Using the invariance of \(\mu\), find the energy to which the proton is accelerated before it escapes.</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>(a) Using the invariance of \(\mu\), find the energy to which the proton is accelerated before it escapes.</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;"></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;"></td></tr>
<tr><td class='diff-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>(b) How long does it take to reach that energy? Suggestions: i) suppose that the $B$ field is approxiamtely uniform in the space between the mirrors and changes abruptly near the mirrors, <del class="diffchange diffchange-inline">\textit{</del>i.e.<del class="diffchange diffchange-inline">}</del>, treat each mirror as a flat piston and show that the velocity gained at each bounce is \(2v_m\); ii) compute the number of bounces necessary; iii) assume that the distance between the mirrors does not change appreciably </div></td><td class='diff-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>(b) How long does it take to reach that energy? Suggestions: i) suppose that the $B$ field is approxiamtely uniform in the space between the mirrors and changes abruptly near the mirrors, <ins class="diffchange diffchange-inline">''</ins>i.e.<ins class="diffchange diffchange-inline">''</ins>, treat each mirror as a flat piston and show that the velocity gained at each bounce is \(2v_m\); ii) compute the number of bounces necessary; iii) assume that the distance between the mirrors does not change appreciably </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>during the acceleration process.</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>during the acceleration process.</div></td></tr>
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Ist426982
http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Magnetic_mirrors_/_Fermi_acceleration&diff=3350&oldid=prev
Ist426982 em 15h52min de 17 de junho de 2017
2017-06-17T15:52:54Z
<p></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 15h52min de 17 de junho de 2017</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l4" >Linha 4:</td>
<td colspan="2" class="diff-lineno">Linha 4:</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>mirror ratio \(R_m=5\). Initially its energy is \(W=1\) keV and \(v_\perp = v_\parallel\) at the midplane.</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>mirror ratio \(R_m=5\). Initially its energy is \(W=1\) keV and \(v_\perp = v_\parallel\) at the midplane.</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>Each mirror moves toward the midplane with a velocity \(v_m=10\) km/s and the initial distance between the mirrors is \(L=10^{10}\) km.</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>Each mirror moves toward the midplane with a velocity \(v_m=10\) km/s and the initial distance between the mirrors is \(L=10^{10}\) km.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-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><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-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><ins style="font-weight: bold; text-decoration: none;">(a) Using the invariance of \(\mu\), find the energy to which the proton is accelerated before it escapes.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-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><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-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><ins style="font-weight: bold; text-decoration: none;">(b) How long does it take to reach that energy? Suggestions: i) suppose that the $B$ field is approxiamtely uniform in the space between the mirrors and changes abruptly near the mirrors, \textit{i.e.}, treat each mirror as a flat piston and show that the velocity gained at each bounce is \(2v_m\); ii) compute the number of bounces necessary; iii) assume that the distance between the mirrors does not change appreciably </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-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><ins style="font-weight: bold; text-decoration: none;">during the acceleration process.</ins></div></td></tr>
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Ist426982
http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Magnetic_mirrors_/_Fermi_acceleration&diff=3348&oldid=prev
Ist426982 em 16h26min de 14 de junho de 2017
2017-06-14T16:26:34Z
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</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l2" >Linha 2:</td>
<td colspan="2" class="diff-lineno">Linha 2:</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;"></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;"></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>A cosmic ray proton is trapped between two moving magnetic mirrors with</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>A cosmic ray proton is trapped between two moving magnetic mirrors with</div></td></tr>
<tr><td class='diff-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>mirror ratio \(R_m=5\). Initially its energy is <del class="diffchange diffchange-inline">$</del>W=1<del class="diffchange diffchange-inline">$ </del>keV and <del class="diffchange diffchange-inline">$</del>v_\perp = v_\parallel<del class="diffchange diffchange-inline">$ </del>at the midplane.</div></td><td class='diff-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>mirror ratio \(R_m=5\). Initially its energy is <ins class="diffchange diffchange-inline">\(</ins>W=1<ins class="diffchange diffchange-inline">\) </ins>keV and <ins class="diffchange diffchange-inline">\(</ins>v_\perp = v_\parallel<ins class="diffchange diffchange-inline">\) </ins>at the midplane.</div></td></tr>
<tr><td class='diff-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>Each mirror moves toward the midplane with a velocity <del class="diffchange diffchange-inline">$</del>v_m=10<del class="diffchange diffchange-inline">$ </del>km/s and the initial distance between the mirrors is <del class="diffchange diffchange-inline">$</del>L=10^{10}<del class="diffchange diffchange-inline">$ </del>km.</div></td><td class='diff-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>Each mirror moves toward the midplane with a velocity <ins class="diffchange diffchange-inline">\(</ins>v_m=10<ins class="diffchange diffchange-inline">\) </ins>km/s and the initial distance between the mirrors is <ins class="diffchange diffchange-inline">\(</ins>L=10^{10}<ins class="diffchange diffchange-inline">\) </ins>km.</div></td></tr>
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Ist426982
http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Magnetic_mirrors_/_Fermi_acceleration&diff=3346&oldid=prev
Ist426982 em 16h25min de 14 de junho de 2017
2017-06-14T16:25:50Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 16h25min de 14 de junho de 2017</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Linha 1:</td>
<td colspan="2" class="diff-lineno">Linha 1:</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>(F. F. Chen ~ 2.12, Fermi acceleration of cosmic rays).</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>(F. F. Chen ~ 2.12, Fermi acceleration of cosmic rays).</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-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><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-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><ins style="font-weight: bold; text-decoration: none;">A cosmic ray proton is trapped between two moving magnetic mirrors with</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-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><ins style="font-weight: bold; text-decoration: none;">mirror ratio \(R_m=5\). Initially its energy is $W=1$ keV and $v_\perp = v_\parallel$ at the midplane.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-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><ins style="font-weight: bold; text-decoration: none;">Each mirror moves toward the midplane with a velocity $v_m=10$ km/s and the initial distance between the mirrors is $L=10^{10}$ km.</ins></div></td></tr>
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Ist426982
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Ist426982: Criou a página com "(F. F. Chen ~ 2.12, Fermi acceleration of cosmic rays)."
2017-06-14T16:10:54Z
<p>Criou a página com "(F. F. Chen ~ 2.12, Fermi acceleration of cosmic rays)."</p>
<p><b>Página nova</b></p><div>(F. F. Chen ~ 2.12, Fermi acceleration of cosmic rays).</div>
Ist426982