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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Hi to everybody,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">It has been a lovely discussion. I just would like to note that it is already taken into account. Our muon production is based on the “light recycling”. Strong
magnetic field and thin target do the same thing. For sufficiently thin target and large magnetic field the phase density of pions is proportional to the magnetic field!!! Is not it the same phenomenon.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">I do not think there is another trick which we could apply to get even more but I would not exclude it. The nature does not squeeze us to Hamiltonian systems
only. <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Merry Christmas and Happy New Year.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Valeri<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif""> map-l-bounces@lists.bnl.gov [mailto:map-l-bounces@lists.bnl.gov]
<b>On Behalf Of </b>Kirk T McDonald<br>
<b>Sent:</b> Thursday, December 20, 2012 6:40 PM<br>
<b>To:</b> Andrew Sessler; Kirk T McDonald<br>
<b>Cc:</b> MAP-l@lists.bnl.gov<br>
<b>Subject:</b> Re: [MAP] Light recycling; Piccione lip<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">Andy,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">If the phosphor simply absorbed the photons that hit it, and did not re-emit them, the brightness of the hole would be the same as the brightness of the phosphor surface – even
though the emittance of the hole is much smaller than the total emittance of the phosphor surface.
<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">[This is the usual version of the brightness theorem.]<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">---------------------------------------------<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">What is special about the aperture lamp is the the photons that do not immediately go out the hole are not wasted, but eventually get out – and into the same transverse phase
space as the photons that got out on the first try.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">In this case, more photons/sec emerge from the hole than we expected from a more ordinary lamp.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">And, the brightness is thereby increased.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">------------------------------<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">When multiple bunches are injected into a storage ring, we don’t succeed in putting them into the same region of phase space. Rather, they are put into adjacent regions (phase-space
painting). This increases the number of particles in the circulating bunch, but the brightness of that bunch is not increased.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">Whereas, the the aperture lamp, a photon goes into the same region of phase space not matter how many tries it takes to get there.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">--Kirk<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">PS Your comments have sharpened my thinking about this interesting process. As a result, I’ve updated my note, with new footnotes 6, 9 and 25.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"><a href="http://puhep1.princeton.edu/~mcdonald/examples/lamp.pdf" title="http://puhep1.princeton.edu/~mcdonald/examples/lamp.pdf">http://puhep1.princeton.edu/~mcdonald/examples/lamp.pdf</a><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">Thanks for prompting me in this way.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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</span><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:whitesmoke"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">From:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">
<a href="mailto:amsessler@lbl.gov" title="amsessler@lbl.gov">Andrew Sessler</a> <o:p>
</o:p></span></p>
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<p class="MsoNormal" style="background:whitesmoke"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">Sent:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> Thursday, December 20, 2012 12:51
PM<o:p></o:p></span></p>
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<p class="MsoNormal" style="background:whitesmoke"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">To:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">
<a href="mailto:kirkmcd@Princeton.EDU" title="kirkmcd@Princeton.EDU">Kirk T McDonald</a>
<o:p></o:p></span></p>
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<p class="MsoNormal" style="background:whitesmoke"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">Cc:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">
<a href="mailto:MAP-l@lists.bnl.gov" title="MAP-l@lists.bnl.gov">MAP-l@lists.bnl.gov</a>
<o:p></o:p></span></p>
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<p class="MsoNormal" style="background:whitesmoke"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">Subject:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> Re: [MAP] Light recycling; Piccione
lip<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">Thursday<o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="font-family:"Calibri","sans-serif";color:black">Dear Kirk,<o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="font-family:"Calibri","sans-serif";color:black">I think I would say it differently and I would appreciate your comment: "Wrong!, Okay, Partially."<o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="font-family:"Calibri","sans-serif";color:black">The photon number doesn't increase at each reflection, so the only effect is that the photon is bounced back and forth until it hits the hole and
gets out. So, the effect is simply reducing the emittance from 4 pi (the whole sphere) to the area of the hole. Even simple to calculate the amplification. So, my view is not a re-using of photons, but a change in desired emittance.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">Andy<o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="font-family:"Calibri","sans-serif";color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black">On Wed, Dec 19, 2012 at 8:36 PM, Kirk T McDonald <<a href="mailto:kirkmcd@princeton.edu" target="_blank">kirkmcd@princeton.edu</a>> wrote:<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">Folks,</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">I have become fortuitously aware of an old trick in the lamp industry that is now sometimes called “light recycling” – with the goal of enhancing the optical brightness of light
sources.</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">Remember, brightness = power / area in transverse phase space</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">(although the opticians don’t generally say it this way, perhaps using the buzzword “etendue” instead of “area in transverse phase space”)</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">In our project, we try to increase the brightness by “cooling”/shrinking the area in transverse phase space.</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">The opticians’ trick is to “recycle” the light so that one photon gets counted many times in the same area in phase space, effectively increasing the power, while leave the emittance
the same.</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">The historical way of doing this (dating back at least to 1936) involves a cylindrical cavity lined with a phosphor (i.e., a fluorescent lamp) with a small slit in the phosphor
to let light out.</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">A photon has only a small probability P to escape out the slit directly after being emitted by the phosphor.</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">Generally, the photon hits another region of the phosphor, is absorbed, and then re-emitted. [The cavity can be lined with a reflector to assist in this process.]</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">On average, the photon bounces around N = 1 / P times before it escapes through the slit.</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">Hence, the steady-state emission of photons by the phosphor surface is N times greater than if the photons flew away on their first emission – as holds for an ordinary fluorescent
lamp.</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">The net effect is that the light coming out of the slit is N times brighter than the light from an ordinary fluorescent bulb of the same output power.</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">The brightness has been enhanced N-fold (with no emittance reduction) to the extent that the absorption and re-emission involves no losses.</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">[I think the lamps in Xerox machines and scanners are of this type.]</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">I’ve written up a pedagogic note on this:</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"><a href="http://puhep1.princeton.edu/~mcdonald/examples/lamp.pdf" target="_blank" title="http://puhep1.princeton.edu/~mcdonald/examples/lamp.pdf">http://puhep1.princeton.edu/~mcdonald/examples/lamp.pdf</a><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">--------------------------------------</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">This trick seems different from what we do to enhance the brightness of particle beams.</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">However, a comment by Fred Mills, dated 9/98, near the bottom of my web page</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black"><a href="http://puhep1.princeton.edu/~mcdonald/mumu/physics/" target="_blank" title="http://puhep1.princeton.edu/~mcdonald/mumu/physics/">http://puhep1.princeton.edu/~mcdonald/mumu/physics/</a></span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">has me wondering if part of the effect of the “Piccione lip” seen on p. 4 of</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"><a href="http://puhep1.princeton.edu/~mcdonald/mumu/physics/lichtenberg_mura-110.pdf" target="_blank" title="http://puhep1.princeton.edu/~mcdonald/mumu/physics/lichtenberg_mura-110.pdf">http://puhep1.princeton.edu/~mcdonald/mumu/physics/lichtenberg_mura-110.pdf</a></span><span style="font-family:"Arial","sans-serif";color:black"> </span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">was to use multiple scattering in the “lip” to kick some particles into a desired area of phase space.</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">That is, perhaps we can say that ionization cooling also includes a small effect equivalent to the opticians’ trick of “light recycling”.</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">What do you think?</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">--Kirk</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">PS The opticians are after big game = use of such tricks to make better solar energy concentrators for photovoltaic energy generation (or even just heating water).</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">In the past, such efforts have not involved brightness enhancement, but only clever rearrangement of light in phase space (as in Winston cones).</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">The next generation of brightness enhancement schemes uses materials with differing absorption and emission spectra to play additional “tricks”. New engineered optical materials,
called photonic band gap materials, could play a key role here.</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif";color:black">If these solar brightness-enhancement schemes pay off, they will be able to fund all of high energy physics....</span><span style="font-family:"Calibri","sans-serif";color:black"><o:p></o:p></span></p>
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