[MAP] Light recycling; Piccione lip
Kirk T McDonald
kirkmcd at Princeton.EDU
Thu Dec 20 20:00:44 EST 2012
Tom,
In the case of the aperture lamp, I agree that there is no reduction in
transverse phase space of photons that pass thru the aperture from the time
they are last emitted by the phosphor to the time the are received on some
distant screen.
For a continuous, monochromatic light source, dE = 0 , while dt = infinity,
so there really is not meaning to longitudinal phase space. It doesn't seem
useful to say things like "the bouncing of the light increases its
longitudinal phase space. If the average time for the bounces is 1 nsec,
and I run the lamp for 1 hour, it isn't useful to say that the dt increased
by 1 nsec compared to the 3600 sec.
As to the "theorems" (such as Liouville's theorem and the brightness
theorem), be careful. These apply only to Hamiltonian systems.
Diffuse reflection is not a Hamiltonian process.
Usually we associate diffuse reflection with some kind of "loss", but the
aperture lamp shows that this is a misconception.
----------------------
Could any of this apply to muons?
I think Chuck is correct that his scheme is a kind of implementation of the
concepts behind "light recycling". It will be interesting to see if he can
make them work....
--Kirk
-----Original Message-----
From: Tom Roberts
Sent: Thursday, December 20, 2012 3:00 PM
To: Andrew Sessler
Cc: Kirk T McDonald ; MAP-l at lists.bnl.gov
Subject: Re: [MAP] Light recycling; Piccione lip
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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