[MAP] Light recycling; Piccione lip

[Tom Roberts]

For the example with light, it's not even a reduction in transverse emittance, 
and is an increase in the longitudinal emittance (as Chuck said, if the source 
is continuous then you don't care about the increase in longitudinal emittance).

After all, there are theorems on this.

Consider a cavity with an infinitely thin wall and an initially isotropic 
distribution of light inside it. Then the angular spread of the light coming out 
of the aperture is 2pi steradians. That, of course, is the same angular spread 
of an isotropic source considered as a beam headed in a definite direction. 
There are geometrical factors that could affect the distribution of light within 
the 2pi sr, based on the shape of the cavity and aperture, the response of the 
phosphor, etc.; I suspect they either cancel out or increase the emittance of 
the output beam. Thick absorptive walls will reduce the emittance by scraping 
(cannot get angles close to 90 degrees), thick walls that are perfectly 
reflective don't reduce the emittance at all (can still get up to 90 degrees).

Also, I don't see how to apply this to muons -- there is no such "phosphor" or 
"mirror" for them.


Tom Roberts


On 12/20/12 12/20/12 - 11:51 AM, Andrew Sessler wrote:
> Thursday
> Dear Kirk,
>
> I think I would say it differently and I would appreciate your comment: "Wrong!,
> Okay, Partially."
>
> 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.
>
> Andy
>
>
> On Wed, Dec 19, 2012 at 8:36 PM, Kirk T McDonald <kirkmcd at princeton.edu
> <mailto:kirkmcd at princeton.edu>> wrote:
>
>     Folks,
>     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.
>     Remember, brightness = power / area in transverse phase space
>     (although the opticians don’t generally say it this way, perhaps using the
>     buzzword “etendue” instead of “area in transverse phase space”)
>     In our project, we try to increase the brightness by “cooling”/shrinking the
>     area in transverse phase space.
>     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.
>     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.
>     A photon has only a small probability P to escape out the slit directly
>     after being emitted by the phosphor.
>     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.]
>     On average, the photon bounces around N = 1 / P times before it escapes
>     through the slit.
>     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.
>     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.
>     The brightness has been enhanced N-fold (with no emittance reduction) to the
>     extent that the absorption and re-emission involves no losses.
>     [I think the lamps in Xerox machines and scanners are of this type.]
>     I’ve written up a pedagogic note on this:
>     http://puhep1.princeton.edu/~mcdonald/examples/lamp.pdf
>     --------------------------------------
>     This trick seems different from what we do to enhance the brightness of
>     particle beams.
>     However, a comment by Fred Mills, dated 9/98, near the bottom of my web page
>     http://puhep1.princeton.edu/~mcdonald/mumu/physics/
>     has me wondering if part of the effect of the “Piccione lip” seen on p. 4 of
>     http://puhep1.princeton.edu/~mcdonald/mumu/physics/lichtenberg_mura-110.pdf
>     was to use multiple scattering in the “lip” to kick some particles into a
>     desired area of phase space.
>     That is, perhaps we can say that ionization cooling also includes a small
>     effect equivalent to the opticians’ trick of “light recycling”.
>     What do you think?
>     --Kirk
>     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).
>     In the past, such efforts have not involved brightness enhancement, but only
>     clever rearrangement of light in phase space (as in Winston cones).
>     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.
>     If these solar brightness-enhancement schemes pay off, they will be able to
>     fund all of high energy physics....
>
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