Stanford University.
>> It's a pleasure, of course, to be here
and to talk to you
and not only a father, [LAUGH] but I'm also grandfather.
And my grandchildren, some of them are
your age, so [LAUGH] I
like to, to talk to them and I like to
talk to you.
Okay, so, by now after the first lecture
you
know how to describe the interaction
between X-rays and electrons
and atoms and matter and you know how to
evaluate this interaction.
So, the next question is how do we get the
photons
to the, to do these experiments and then
later on you will
see how you put these photons on your
cellphone, you will
see the instruments that have been built
here and the full NCLS.
So, but I will concentrate on this path
so,
I will discuss initially why we want an
X-ray FEL and what
we can do with it, then the basic
properties of
the radiation from accelerated
relativistic
electrons, this is the fundamental
process.
Is similar to what you have in an
atomic laser, the fundamental process is
the transition
between different states, different
electron energy
states, here is the radiation from the,
these accelerated relativistic electrons.
And then I will go into more detail on how
the LCLS works, the works
based on a FEL collective instability, a
kind of self organization effect.
And then I will discuss some of the
present work which is being done to
further improve the X-ray FELs okay.
So, why, I mean people have been pushing
for a long time to get an X-ray laser,
and in particular X-ray FELs feel like two
lasers.
Are interesting because they are fully
tunable from about 10 to .1 nanometer,
they have transverse and longitudinal
coherence, high peak power, tens to
hundreds of gigawatts, hopefully we will
get to the terawatts soon, and the pulse
length can change between a few
femtoseconds to 100 femtoseconds.
And so because of this property, in
particular the last one, they are the
only instruments available to explore
atomic and molecular
signs simultaneously the characteristic
lengths
scale one angstrom autonomic radius and
The characteristic time scale of atomic
and molecular phenomena, about one
femtosecond,
and with this, we can really look
at atomic and molecular weld in great
detail.
Using conventional, atomic-based laser, we
can do the ultra-fast
side, there are laser that can go to the
femtosecond, even nanoseconds.
And with X-rays, including X-rays, we can
look again
at matter on the angstrom, length scale
but until the
SCLS started to work in 2009, it was not
possible to really explore this region at
the same time.
And of course this is a big next step
forward because,
normally we look at measure with our own
eyes, and with that
we have a resolution in a lens of this
kind
and the resolution in time with our own
eyes is about a fraction of a second.
So,
from what one nation gave us, building
microscopes,
and then lasers, and now electrolaser.
We have made a big step, we can go here to
here and from
here, to here, we can see things that
otherwise it would be impossible to see.
So, we are expanding our capabilities, we
are supermen
okay.
The transverse coherence and the large
number of photons gives us new
possibilities of imaging, and nanometer
and sub-nanometer scale.
We can follow the dynamics of this
process, we can start the non linear
phenomena, and so there is a whole new
world for us to, for you to work on okay.
so the laser was an important step in
this direction, and it was invented in the
1960's.
This is, you can see that Maiman when
he built, well, 25 years after he build
this device the first ruby laser.
And today, this kind of laser covered the
region from
infrared to EUV with very high intensity
and short pulses.
From the time the first layer was built in
the 1960's
people looked at the possibilities of
developing the system to go
to the X-ray, region and the using this
type of laser
it's really very hard to do it and there
are two reasons.
One is that the atomic level that you want
to
excite, you want to have your population inversion
range of one to 10 KV and in addition the
life time of this quantum energy
level is very short.
And if you put the two requirements
together, it comes out that
you really need an extremely large input
power to
generate the population invasion in the,
the laser, laser action.
In fact this was started in the bay in
particular Livermore
they made an estimate, the The
transition, the life span for the states
is about one
femtosecond times of the square of the
wavelengths in action so at one
angstrom you have one femtosecond
In addition you are this energy that you
need to burn so it really was very hard.
So, someone in Livermore came up with
the idea of using a nuclear
bomb to drive an X-ray laser In fact, they
did it.
[LAUGH] And you can find some more detail
on this story in this paper.
I don't know how much of this experiment
you can
really see in the open literature but it
has been done.
And it was also, pushed by the idea that
some
people had at that time about the star
wars defense initiative.
To, put up one of these X-ray lasers in
space
to kill incoming missiles, and you saw an
incoming missile
you were to explode the atomic bomb, that
would generate
X-ray beam, and the X-ray beam would
destroy the missile.
Even if you can do an X-ray in this way I
don't think
you can, use it for most of the
experiments that we are, doing today.
And, that problem was terminated when star
war was ended.
And there was an agreement to reduce the
number
of atomic weapons to not to put them in
space.
That alternative was to create a small cylindrical
plasma or some material like selenium.
In some cases you could also confine this
plasma with a magnetic field to help
the process and then shine a very
high-powered laser on this and start
the process of stimulated emission and
this was more successful.
And in 1985, two of these type of lasers
operated
around 20 nanometer with small gain,
but they did generate laseing.
And so more work has been going on in this
direction, there has
also been also some recent progress but,
in the end you have two problems.
This system is much smaller LCLS that would
see, LCLS is kilometer size and very
expensive.
This is much smaller, they can fit in a
lab uh,they might even fit in a university
lab.
On the other hand is not tunable, they are
related to a limited number of lines
and the amount of power you can get is not
comparable to what we can get at LCLS.
So, it's an interesting type of web, but
is not a real competition to LCLS.
So, seeing people seemed to want an X-Ray laser, we looked at the
possibility of doing it using free
electrons, and it was mentioned
before, I may a proposal to use the
[INAUDIBLE] and that led to
the operation of LCLS in 2009.
Paper appeared in 2010, and more recently
there has been the SACLA,
the Japanese, X-ray FEL which started
operation a couple of years ago.
And the, others, we saw are under
construction,
in the Switzerland, in Europe, and in
Korea.
And they'll add also two X-ray in
operation one is FLASH, and
one can cover the region
down to about four or five nanometers.
And, all of this has been pushed by the
idea that you can see very well in this
report from DOE, during the half-century
since the laser was conceived.
And the use of coherent light has become
an indispensable part of our world, we all
know, I mean, from, from this laser
to a DVD or a CD we use coherent lasers,
coherent light everywhere.
And is really pushing a trillion
dollar global economy.
So in today's world, the development of
tools and techniques that
use coherent light and even shorter
wavelengths, it's assuming an encasing
importance.
And now, the short wavelengths can be as
short as a fraction
of one axle, so the desire of your EOE has
been realized.
Here, you can see a comparison between
different X-ray sources.
And the units are in,
brilliance, or brightness, some people use
brilliance, some people use brightness,
which is the number of photons that you
can get per second per millimeter,
squared, or the source brilliance squared,
the angle of the radiance and
4.1 percent photon energy
bandwidth.
And so you can see on this
scale the conventional laser, they can
have a very high big
brilliance in the region around one
electron volt.
For X-rays, you really have to go to
central and radiation
sources based on storage links, and if you
really want to go up,
I mean, when LCLS started to operate in
2009, In the
X-ray region around 10 to the four
electron balls.
In a one night this big blindness has
went up
by nine orders of magnitudes, so this is
really, a remarkable
event I mean, doesn't happen often in
science that you can
change one important quantity by so many
orders from magnitude.
So, this is essentially what I already
said.
So, since atomic system
cannot go to the X-ray region
we started looking at the possibility of
using Accelerated electrons.
And accelerated electrons been used for a
long time to generate X-rays
you can get radiation by accelerating an
electron uh,by
simply moving them
in a magnet like you do iin a synchrotron
storage link or in an undulated magnet, we
talk about this more.
You can get radiation from an electron
with constant velocity and
not accelerated, if the velocity is larger
than C over N.
The velocity of light in the video in
which we you are moving, If you are
stopping or starting a charge, so the
acceleration is a kind of Delta
function and this is the base for all the
bremsstrahlung sources.
And so, if you go to a dentist and
he takes a picture of your teeth, he's
using this.
It's much smaller than what we have at
LCLS
I mean the typical X-ray tube, in a
dentist's
office is about one foot long and it costs
5k.
It's several order of magnitude different
from L.C.L.S then
you can use a cost of velocity again, but
in
neurology use periodic systems
[INAUDIBLE].
All these kinds of radiation can be broad
band or narrow band.
Most of them are broad band except when
you include, you introduce periodicity.
So you select a narrow band by
interference.
If you want to evaluate the radiation
generated by
electrons in all of this situations you
can start from
the Lienard-Wiechert fields, the reference
for this is Jackson,
a book that I'm assuming you all know very
well.
So you can see the near field, the
radiation field, the magnetic field is
perpendicular to the electric field and
to
the N is the direction of
observation.
One important point to observe in this is
that if you look at this denominator.
This depends on the angle between the
directional observation, and the
velocity, so these would be the velocity,
this is where you are looking at.
And this is a very strong dependence, and
if you assume that the angle between
these two direction is not very large
we can approximate the denominator of this
formula.
1 plus gamma squared theta squared, theta
is the angle
over 2 gamma squared, so if theta is 0, or
is more less than 1 over
gamma, you get the factor of gamma to the
6 in the numerator, which is big increase.
But if gamma, if gamma theta is larger
than 1, this particle becomes 001.
So the radiation is essentially limited it
to an angle
1 or gamma and is strongly pointing in the
forward direction.
In most cases more than the elective field
or the magnetic field, we want
to know what is intensity per unit
frequency and per units of the angle.
This is given by this formula.
Again, you can find these in Jackson, and
better is the velocity of the electron.
All of this is now evaluated several
times.
And this is very similar to the Fourier
transform of the velocity.
From looking in the forward direction,
velocity would be the transform velocity.
So, this quantity is an important
quantity, essential the Fourier
transform, the square or the Fourier
transform of the transverse velocity.
So, by changing the velocity, you can
really, changing the
trajectory, you can really change the
characteristics of the radiation.
An example which is known, has been known
for
many years, is the Synchrotron radiation,
and in this case,
you have a broad band extending up to
a critical frequency which grows strongly
with gamma.
And this is the basis of all these
light sources you
can have a spring gate you can add the
SRF.
But they're all similar, the only quantity
that can change is the, this point
where the intensity starts to decline
exponentially
which is defined by this critical
frequency.
>> [Inaudable student question].
>> Oh, this is the, if I have an observer
here and these electrons is moving on this
orbit, and the
radiation is meeting a small angle one
over gamma, if I
look at these, I can always see radiation
for the time.
Corresponding to go, to this arc, which
corresponds to another two over
gamma.
And so it's a very short time.
>> How short is it?
>> Well, this is the, what you.
The formula gives it to you.
This photon starts from here and gets to
you at the velocity of light.
For this photon you have to wait for the
electron
to arrive here, and that will depend on
the velocity of
the electron, and then you see let's come
here, but the
last part of the trajectory of the photons
is essentially similar.
So you have the difference between the
time that you need for
the electron to go to this arc or
responding to an angle to
over gamma, and the difference that, in
the time
that it takes to photon to go from here or
to here on the projection or distance.
And this gives you the sworbola that
you see you
have frequency corresponding to this.
And this is the frequency here 
the observation times, the times.
The, delta E delta T must be H Bar
over 2, and so you have the delta T
and from these you can evaluate the delta
E, and so you can evaluate the frequency.
>> So the radius is typically on the order
of 100
meters or so, and what kind of cameras are
we talking about?
>> Well, if you take APS.
Is what, six GB?
The gamma is over ten thousand.
And springate is a little bit larger
energy.
So gamma is typically in the range of ten
to the four or more.
So that's a big factor.
And that's why.
By increasing the
the electron energy, of course when you
increase the electron
energy you tend to increase the radius of
the ring.
So, it's really not increasing like gamma
cubed, but more or less like gamma
squared.
But still that's a big factor which pushes
this
the maximum photon that you can see, two
higher energies.
In 1951, the professor here at
Stanford Hanz Moss,
looked at another possibility.
He proposed to use a long array of
alternating magnetic fields.
So if I look at this, you will have,
North/South, North/South, and so on.
To generate an electron trajectory.
If I send an electron beam in this
direction.
So the electron beam is mostly moving
along the undulator axis.
[COUGH]
The trajectory will be a sinusoidal,
because of the changing magnetic field.
In the sort of thing you keep going around
a circle, in
this case you do an arc of a circle in
this field then.
You bend the particles in the opposite
direction in the next pair of magnets.
So what you get is this kind of sandwiched
all those trajectories.
So now you're imposing your periodicity,
and instead of a
wide broad band addition, you should get
a narrow band addition.
Most of the radiation is coming from
the points where you have the maximum
acceleration.
So you have these points.
And most evaluated the radiation, and also
consider the possibility
that if the wave length is longer than the
electron bands.
All these electrons should radiate
essentially
together, like a big super charge.
If you have any electrons in a band should
be shorter than the wavelengths,
you can get an intensity which grows like
NE, the number of electrons squared.
And so, we evaluate all of this.
And a few years later he did an
experiment,
he built one undulator with a period of
four centimeter.
He used an electron beam from a linear
accelerator at Stanford.
Stanford was really the place for this
linear accelerator were being developed.
And it's interesting to notice, if you go
back in history.
Stanford at that time, was a, place where
there was a lot of interesting X-ray
physics.
And most of these accelerators, initially
were
developed to generate, to produce X-ray
sources.
Then the interest moved to high energy
physics.
We had the big linear accelerator.
But in the end, it came back to
X-Rays.
So so he built himself an undulator, and
used an electron beam.
And they looked at their addition and they
saw that if the beam energy was low,
so the additional wavelengths was large,
in the millimeter region.
You would see a lot of power, in measure
in excess of one watt.
And increasing the beam energy and sort of
using the
wavelengths of their radiation you saw a
much smaller intensity.
But you saw a little bit of radiation.
So meanwhile the proof of principle that
you can generate
Narrow band radiation with this system.
And this was done again, the beginnings of
the 50s.
So let's look a little bit in more detail
of this kind of addition.
These again an example of an undulator
you'll see that the magnetic field
direction alternates North, South, and so
on.
And if I look at the magnetic field
in this kind of structure I find this
formula.
So there is well, the main magnetic field
is in the y direction,
there is no field in the x direction, at
least if you stay near the axis.
And the magnetic field in the vertical
direction is periodic k u is
the undulated way number is two pie over
the p dot of this.
Magnetic structure which we will call
lambda u.
And z is longitude in our axis, so
electron b which will
send through most several last will also
be in the z direction.
This is the velocity before it tends to go
later.
When you enter in later, in addition to
these velocity in the z direction.
You have this transfer velocity, you have
this weak link trajectory.
You also have to satisfy the Maxwell
equation, there's more longitude in our
Component.
But then beyond other axis we can
approximate this cost with one and
we can approximate this with KUY and do
the linear approximation.
So, with this field we can evaluate the
trajectory, at least for electrons near
the axis.
And we find, of course, the next component
of the velocity, which is given by this
formula, is, again, periodic, with a
periodicity of the undulator and is
proportional to this, quantity K which is
the undulator
parameter, is really in physical terms the
undulator vector potential.
Normalized to the length of this energy.
And this is an important quantity.
If you put in the usual, units of Tesla
for the field and centimeter
for the period, you can write this point
93 which is almost one.
The field being Tesla, landing you in
centimeter.
So this is a number typically of the order
of one
or a few, for a conventional undualtors.
So this gives you the transverse velocity,
of
course, the longitudinal velocity which is
beta Z.
Before is, simply 1 minus 1 over gamma
squared, before you enter the undulator.
becomes, smaller, you have this additional
factor due to
the fact that you have a transverse
velocity and so.
You're putting some energy, some momentum,
from
the longitudinal direction into the
transverse direction.
And so the longitudinal momentum and
velocity will decrease.
You have this factor here.
[COUGH] You have also, an addition
periodicity at twice the undulator.
period, and all of this quantity goes down
like 1 over gamma squared,
so when, before you enter the undulator k
is 0, and you see 1 minus
1 over gamma squared 2 gamma squared.
And, this term here is not I mean it
averages to 0 in a few periods, but.
It gives an additional periodicity, and
gives rise to
the radiation, generated by this as we
will see, in, in a moment.
Okay, so this is the electron trajectory,
it's the
velocity from this you can evaluate the,
the trajectory.
In all directions.
So, now because of the periodicity you
have
this interference effect tht we were
discussing before.
Again, if I'm looking in the electron
data, data is the angle in respect to
the axis and undulator, which is also the
main velocity of the electrons.
If I look at the the photon emitted from
this point it will take a certain time
to arrive to the observer, and the photo
emitted
at this point it will take a different
time.
And so the difference in sign is due to
the difference in velocity between the
electron and the and the light, the
electron takes a certain time to go
from here to here, and danger is this
different due to the, fact that this
photon had to do some extra to move a
little bit on this extra trajectory.
And if you evaluate this, you get this
formula.
This is the difference in arrival time and
the observer.
But now, if this difference is equal to
an integer multiple of the period of the
light.
Integer multiple lambda over C, you get
positive interference.
So you can define a wavelength at which
you expect to
see a maximum of their addition, and it's
defined by this formula.
And for the electrons and small
angles, which is
typically the case, you can approximate
this formula in this way.
You add the undulator P at 1 + K^2 / 2,
then you add this factor gamma^2
to the squared wavelength increases with
angle, you move to the red.
And, you add this factor to our gamma
square and then you add this extra factor
of
n, and it's equal to one for the
fundamental but you can get also all the
harmonics.
We'll be mainly concerned today with the
fundamental.
And so for the fundamental we call the,
radiation wavelength's, Lambda-R.
So now we have our, spectrum our we know
where
we should expect to see the intensity and
now we can evaluate the formula for
the intensity per unit frequency unit
solid.
Own axis.
This is given by this formula, you have
a bunch of constants.
It goes like the square of the number of
periods, the square of the electron energy.
Will this factor which gives you the
dependence of the magnetic field.
Of course if there is zero magnetic field
you get zero radiation.
You have this factor F, which depends
again on the
money that you are considering and this is
okay.
And, and the magnetic field.
And then you have the real spectrum which
is a sinc function.
So, the argument is by number of periods, the change,
let's look at the fundamentals.
So, this gives you the intensity of the
frequency omega,
and this depends on the different between
omega and omega R.
Omega R is the quantity that we, obtained
before, and of course this is a spectrum
which
has a peak when omega is equal to omega
R, this quantity is one and then it
oscillates.
And the weights of the, of this line that
we get,
is given by one or the number of periods.
So, the more periods you put the undulator the narrower is
the line that you get.
If I look over their harmonics I have an
extra factor remaining.
The harmonics tend to be narrower than the fundamental.
Typically, for an X-ray of fiel the
number
of periods that we have in the undulator
is
between 10^3 and 10^4, so the fundamental
line
width, is in the range of 10^-3 or 10^-4.
So this is an important formula, yes?
>> So is this the sync argument?
If I, if I think in terms of free
transformers,
sync is, is always related in 
form to rectangular functions.
So how can I think about it.
Is there somewhere a rectangular function
appearing the
physics that transform, and get them this
line shape?
>> Well this is the, well this comes from
the in, in a way, that is true,
because, you have this radiation only
during the time,
when the electron is within the undulator.
Okay?
So we had nothing before, nothing after.
And you were a kind of square
pulse within the square pulse you
have periodicity.
But, that defines the [INAUDIBLE]
>> [INAUDIBLE] narrows my bandwidth?
>> Yes.
If I go back to the [COUGH],
no, I'm going in the wrong direction.
If I go back to, what is it.
This formula over here.
The integer in here is given between minus
infinity
and plus infinity, because we don't know
what beta is.
But when you apply these to an undulator,
here you have essentially
the transverse component, and the
integration
is extended over over the undulator
lengths
>> What is n again?
>> N it's the direction in which you look
at the light, okay?
So on axis, I mean this would be
essentially better transfers.
This would be the, unit vector in the Z
direction, the main propagation of
the electrons and, this is the transfers
velocity which is only different from
zero.
When you go through the undulator, so that
gives
you the square faction that you, that you
were mentioning.
>> I think about this formula here in
terms of, you observe a light
flash, and then you transform the light
flash frequency space which gives you the
spectrum.
>> Yeah, yeah.
>> But how does this double cross appear
here?
How does that come in?
>> Oh, [LAUGH].
>> Without, you know, other interjection,
is
there an intuitive explanation for this?
>> Well [LAUGH] Okay.
[LAUGH].
You have to start from
okay.
The, in reality, I mean, there is a
complicated process
because you have to start from this, then
you go into
frequency space, you have to take the
square of the
electric field, and you had to do a lot of
manipulation.
And you also had to do a lot
of manipulation because in this formula
you have
the retarded time and you want something
that
does not include the retarded of the
time.
Because it makes calculation very
complicated.
So if you go through all this process and
Jackson doesn't.
So [LAUGH] you end up with this.
But in, in a way I essentially test you
that if beta
is a constant
you get a kind of delta function.
But if beta is a period function, then you
get periodic Fourier transform.
In a more physical term, [COUGH], if I
look in the tail of the radiation,
I see impulses of light and they
are coming mostly why did I do it,
[SOUND] Okay, each time the electrons go,
this is the point where the acceleration
is maximum, and this is the next point.
So, if I look at the light coming out, I
see a series.
Or impulses, each one is short but there
is a certain periodicity.
Okay?
And, this series of pulses has a limited
duration, which is a little length.
So, when you put it all together and you
do the
Fourier transform, or this almost delta
function, spikes with that periodicity.
You end up with this.
>> So if there would be perfect delta
functions
then you should get infinite amount of
harmonics, right?
>> Oh yeah, you should, yeah.
And you factor in, you get harmonics
because this applies to any value of N.
Now, the importance of the harmonics depends
this factor here.
If K is very small
K or gamma is less than one.
Then you get essentially only the
fundamental, but
if K is large, like in LCLS is three.
Then you get very strong third harmonics,
fifth harmonics.
They can even be stronger in some cases
than the fundamental.
>> So when you say k is strong, you mean
the magnetic field is strong?
>> Magnetic field is strong.
>> Which means that.
>> Well, K depends on the magnetic field
and the period, yeah.
So for a, a LCLS, is just to give an
example, is K about three.
[COUGH] And you want the last K, otherwise
otherwise, this factor is going to kill
you.
[SOUND] Okay, so, just to again, to, give
you an example.
Let's look at the LCLS case Gamma is 3 times
ten to the four, is about 15 GV.
Then go out to the value, the undulator
period is 3cm K's three.
You have 3,500 periods.
The wavelength is one angstrom.
Delta mega, or omega is three times 10 to the minus four.
And, you also have you ca, I can also look
at this in another way.
As the electron propagates, through the
undulator, it generates a wave train.
And, the length of this wave frame is the,
wavelength
of the radiation at which I am emitting,
times the number of periods.
So the radiation that I see, if I had only
one electron, I would see the single wave
frame, which in this case, would have a
length of 0.3 microns.
That's about one femtosecond.
Or if I have many electrons would have
a lots of these wave frames which super
impose.
And depending on the way, in which they
super impose my output radiation can be
really, really different and this is how
to
optimize that is really what an FDL does.
I can think of a case in which I
have one electron emitting one wave frame
and then I
have another electron following by Lambda 
over two, and if
I look at the two, the two will cancel
out.
So, for the distribution of electrons in
which
all the electrons are separated by half
the wavelengths.
They generate wave frame shifted by Pi,
and I would get zero.
But if all electrons, are in a distance,
shorter compared to the wave
length, they will get something which goes
like, the number of electrons squared.
The number of electrons is typically ten
to the ninth.
So I have a range of values which goes
from zero to ten to the 18 and
how to play with that is really what we
do.
Okay before I go into more detailing,
these is the next step.
In this process, after months, came when
John Madey, he
was also, here went to Stanford looked at
the possibility
of stimulated undulator radiation, he
immediately called the stimulated emission
of bemstrablung, in a periodic magnetic
field which is an undulator.
And, the idea was if you add these
electrons going through an undulator or
electron velocity generation radiation,
but if I input an additional
electromagnetic wave, the frequency, the
frequency corresponding
to the frequency of the undulator
radiation, let's say the fundamental.
Then, all together, I can get stimulated
radiation,
and I can get more photons out [COUGH] And
again, like
I have to do in the theory E
and
undulator, which was about
five meters long conducting helical
undulator, and they, the first thing that
they did
was to send to an electron beam that was
from a superconducting linac.
on campus here, in
in the lab on campus.
And
together with the electron beam they
copropagated a CO2 laser.
And they did observe, stimulated emission
of radiation, so they measured gain.
The gain was about 7%, and the
theory that been developed by Madey was
only good in this
range, and he consider on any occasion, in
which going through the undulator.
You have a small change in the
electromagnetic
field so it's called the small gain
theory.
[COUGH]
An interesting result from the, this
theory which I call the quantum theory,
is that the end result again that you
would get in this input laser field.
Was not dependent on Planck's constant.
So you start with a Quantum theory, you
end
up with something that doesn't contains H
or h bar.
So there is something that tells you that
in reality
the effect is a classical effect is not a
Quantum effect.
Another result is that if you apply this
theory which was valued
for linear changes in the magnet, in the
intensity of the electronic radiation.
And you try to scale it to, reach the x
ray region, wasn't that good.
Good.
The scaling is not really favorable.
You are in a situation not as bad, as the
one with atomic laser, but almost.
Okay.
But this was another important step.
Now before we go on we need to say
something about the photon phase space and
the coherence.
So
if we generate photons and we want to
look,
the photon density in a free space area x
p x y p y.
Which is defined, by the certainty
principle.
This is the minimum free space area that
you
can get, in in this two planes, xpx, ypy.
And, if all photons would be in this
area, then you would transfer the coherent
photons.
They would be essentially the same photon,
okay.
And we know that you can have, as many
photons as you, want in this volume.
Because they are, photons are bosoms, and
not failures.
If instead of The momentum, transverse
momentum
we use the corresponding angle theta, the
transverse momentum over
the total momentum, we can write this
condition also as delta x delta
theta must be larger or equal to lambda
over 4 pie.
So lambda for pie is the minimum value
that you can have, for this product.
So if you transfer this beam, this photon
beam, through a nautical system, you have
lenses,
mirrors, and so on, you can exchange x and
theta x, but the product is an invariant.
So, these are useful quantity, and the
coherent part for the photon beam, the
diffraction limited part, is restricted to
these minimum phase space area.
Sometimes this quantity can also.
>> It's also called emittance and is a
useful quantity because it is an
invariant when you transport the photon
beam through an optical system, including
focusing elements and if you neglect
losses in the system.
For
the longitudinal case, we can write
something similar.
And we know, what is the delta t, in this
case.
Or if we write it in terms of omega.
We know again that delta omega over omega
is 1 over Nu.
It's given by, the language is given by
the number of periods in the undulator.
And, so if you want to obtain.
Photons which are contained again within
this part of the face base.
And, remember that the photon wavelengths,
depends not only on
the beam energy, but also on the angle of
emission.
If we want to stay within this bandwidth,
we must limit.
The angle of emission that we observe.
So we can define, a critical angle
corresponding
to, an increase in wavelengths given by,
these line
widths, and this is the ratio, the square
root of the ratio of the wavelengths to
the.
And u lambda u which is the undulator
lengths.
Now if you want to consider the fraction
limited
radiation, together with this angle, me
must associate a red
use for this photo beam and again, we have
this
relationship that the product must be
lambda or for pie.
So, for the radio, so this photon source,
we have the
square root of the lambda times the undulator lengths or for pie.
So these are important numbers, if we
are mainly interested in coherent
transverse coherent photons.
For the case of LCLS, given on the little
lengths, the wave lengths.
We obtained that the physical angle is one
micro radon, so this
gives the angle a spread for this coherent
photons, and the
corresponding transfers, both sides, still
micro.
So the undulator radiation is really an
extended source undulator in our case
of LCLS is 100 meters long, you can get
radiation from all of these 100 meters.
But to first approximation you can
consider it equivalent for the coherent
part.
To a source at the center of the undulator
with this radius, and this angle aperture.
So the next question is, since we know
the intensity per unit, frequency per unit
solid angle,.
And from this data here we can evaluate
the solid angle.
How many photons do we get in there per
electron?
The numbers, defined in this photon
source, I
have the electron going through, just one
electron
for the time being, then we'll see out
what transforms into when you add more
than one.
And if I look at the radiation outside the
undulator I'm looking at the far field.
Okay.
This radiation, has an angle at aperture
and is like if
it would be coming from a source which has
this radius.
Okay.
You can't be this, because it's the
essentially the uncertainty principle.
So, the next question is [CROSSTALK].
>> [INAUDIBLE].
>> Yeah.
This will be the fraction image of
radiation.
You'll get more radiation from the
electron,
because you'll get radiation out of these
angle.
But if you want to look at the greater
pattern.
Which is the one that we want, the one
that we want to amplify in the field.
This is the, so, I since I, have the
formula
giving me the intensity per unit frequency
per unit solid angle.
I use this solid angle, defined by delta
critical.
And I use my language which is one over
nu, and I evaluate the number
of photons, coherent photons, that I get
for
and electron from in going through the
undulator.
And this is a very nice one, huh?
Because it's.
Essentially depends on the fine structure
constant.
There must be a dependence on K because if
there is zero magnetic field I should get
zero
but if K is of the order of one, this
number again is of the order of one.
This function again for reasonable values
of K is of order one.
So, to face approximation, this is number
is of the order of
alpha, which is on the order of ten to the
minus two, is
one over 177, it is a universal constant,
it doesn't depend,
on the beam energy, it doesn't depend on
the number of periods in the undulator.
It's a very nice formula because of that.
If I send an electron to an undulator, and
I want to see how many coherent
photons I get, it's about ten to the minus
four photons per electron.
So, if I add an undulator in a [UNKNOWN]
where I do not have
any amplification, and I have a beam with,
I don't know, ten to the
nine electrons, a bunch an electron bunch
ten to the nine electrons going
through an undulator in a sort of ring, I
get ten to the seven coherent photons.
Sorry yeah ten to the seven coherent photons.
At this factor of ten to the minus minus,
more or less.
Okay, so this is a handy formula that
allows
you to, evaluate how many coherent photons
you can get.
yeah, it doesn't depend on anything.
Wavelengths, electron energy, and the
little lengths, and so on.
So, yeah?
>> I'm a little confused.
Because, before, you said that all the
electrons in the bunch could emit
collectively.
>> This is the.
>> This one.
>> Alright.
[SOUND]
>> [LAUGH] Next slide.
[LAUGH] Okay.
So, usually you don't take one electrons.
I remember seeing one electron in a
[INAUDIBLE] a long time ago.
And you'd see the radiation, at some point
the radiation stops because the electron
is lost but in most cases we want have a
lot of electrons, so if
I'm sitting at the exit of an undulator,
what I see is.
All these wave trains coming toward me,
and they are
superimposed depending on the initial
phase.
So, depending on the position of the
electron, relative
to the wavelengths or radiation at time
zero.
So, if these electrons have no
organization.
They have distributed more or less in a
uniform way inside the electron bands.
You get a random superposition of these
raying waves.
It's, like, similar to what you get from
one of these lines.
And you'll get an intensity, which is only
proportional to the number of electrons.
Okay?
In theory, the electron distribution well
is perfectly uniform.
So for each electron you, add another one,
separated by lambda over two.
For a uniform electron caravan, you get no
radiation.
Okay, you, you don't see anything.
Fortunately, now with electron beams, we
don't have this perfect uniform
distribution.
So there is some randomness in the
longitudinal distribution, so
there is some randomness, in the
distribution of this wave
traits, and you will get a component of
the banshee factor corresponding to the
radiation wavelength.
But, you'll get an intensity proportiona.
This is essentially
spontaneous radiation, you have no
organization.
But, if you could organize, all the
electrons so
that they are within a small fraction of
the wavelengths,.
Then you would be in a situation like this
and the intensity goes up tremendously.
If you really organized them well, you
would get a factor in a
square, as I said before, an instant to
deny, or something like that.
So, to describe this electron beam, we can
introduce a an order parameter which is
called the bunching factor which is the
sum of all electrons and the displaced
factor.
This is the relative phases of the
wavelengths which is
related to the time at which the electrons
enter the undulator.
And the undulator entrance in this case,
okay.
So for perfect order, will there be one?
And for perfect disorder, we will be at
zero.
Okay.
Now at one angstrom about ten to the
three, ten to the four for electron and
wavelengths.
And so if you look at this distribution,
you always get some value of B which is
certainly not one but
it's, small compared to the minus four,
compared to the minus five.
But really would like to have this factor
to be one.
So how do we do that?
How do we squeeze all of the electrons in
about one-tenths of the wavelengths?
Then this electrons can still be separated
by the wavelengths.
But it should be, like kind of, one
[UNKNOWN] in which we have little bunches
of electrons.
Very small, and also all separated by
lambda so,
these were the fieldas. It does this
organization for you.
formally, if I go back to the intensity
distribution and
frequency and angle, if I want to evaluate
this for a.
Electron B I like to do first the
integral, then the sum, then take
the square, and, in doing that, I have to
do
a lot of consideration, in particular I
have to consider the fact
That the electron trajectory can be
different.
The transverse position of the electron
can be different, but even if
I assume that all the electron
trajectories are equal in the simplest
case.
Then I would get this integral out of the
one I had before.
So the total intensity to first
approximation can
be written as the, single part of that we
call intensity, times the square of the
bunching
factor, times the square of the number of
electrons.
For instance, if I assume that I have a
Gaussian.
Distribution in the longitudinal
direction.
Gaussian bunch, with an rms length sigma
zero.
For this factor and a, and E squared, B
squared I got this form, all right?
So, if the wavelengths is, much smaller
than
sigma, the bunch is long compared to the
wavelengths.
This is essentially 0.
I cannot like this, this drops down very
fast, and I get Ne.
By default my electrons are within a
distance smaller than the wavelengths.
Essentially this is one or near to one and
I get this factor in this square.
How much time do I have?
Got about a half an hour.
>> Oh, Okay.
Okay, so we had to also introduce the
effect of the fact that not all electrons with
the same trajectory.
The velocity can change, because of the
way the
electron arrived at the undulator, when we used this
formula.
Without the better X0, we assume that the
transfer's velocity is
0 at the undulator entrance and that is
not the case for all electrons
and also that the vertical velocity is non
0.
So we have to include now certain
characteristics of the.
Electron beam.
And we can again look at the phase pace
for electron beams like we did before.
If I write the same formula, I could write
it as before but
now the wavelengths would be lambda
contour over pi and that's very small.
Our beams are well above this so I
cannot get a coherant electron beam.
But, I must still match, if I want to get
good radiation out of the undulator.
I must match the electro beam face space,
to the photo beam face space.
The photo beam face space is defined by
lambda, the
wavelength of the radiation, that I want
to look at.
Which is.
Even at one angstrom is much larger than
the quantum wavelength, so these I can do.
I know how to generate the beam that
satisfies this, the phase base earlier in
the transverse
direction for the beam defined by the
position
and angle is smaller than the photon
free space.
but, I could not do this, at least today.
So anyway, this is an important condition,
to get good radiation.
And.
I also have, a longitudinal face based
condition,
because again, if my energy is changing
too much the wavelength is regulated
by each electron, changes a lot, so what I
require,
an additional requirement on my electron
being is that the delta.
Lando and lambda due to an electron change
in
energy, or due to an electron change in
angle.
Or due to an electron change in transverse
position, because the magnetic field is
the cost therm
so when I move our faxes, the magnetic
field will go up, will increase.
It's again, because of Maxwell.
So I can relay the transverse position to
a changing K.
And altogether I must ask that all in
all, this should be smaller than the line
width.
So add this requirement.
And I can define an effective energy
spread due to the beam emittance.
The change in theta and in the [UNKNOWN]
position.
And I have to add that to the, real
energy spreading
the beam, and then see what that does to
the intensity.
So if I make a plot, again of
the intensity distribution this is near
the fundamental.
For 1 electron in ideal beam, I would get
this curve.
If I have an electron beam, with one
tenths of the,
with an energy spread corresponding to
one-tenths.
Of the language of the radiation, I would
get essentially
the same care, but if I have , total energy
spread corrresponding
to 1 over nu to the language I get this,
and then if I go to twice that I get 0.
So, you can immediately see.
How important it is to add an electron
being satisfying these conditions.
Okay, so now we can go on to the FEAs.
So, we say we would like to add these
electrons
well organized in micro banshees shorter
than the wave lengths, one angstrom.
Separated by one wavelengths.
How do we do that?
That's hard to do because we're talking
langstons,
And have no way of doing that ourself.
The emission of electrons from a catalyst.
Not a very controlled process.
They come out whenever they like.
And so they time the distribution.
But we we are lucky in this case
[COUGH] because if we set up our undulator
and our electro beam.
And we make sure that the electro beam is
good enough so it
we are near this kind of situation.
The electron beam self organizes.
This is what we started a long time ago.
And so, we tend to evolve naturally from a
disorderly electron beam to an electron
beam which has these
properties of being nicely organized, that
is the self-organization
process, which is in this case is a good
process.
Self organization process can be very
good.
We are a self organization process and we
like that.
These and other examples are a good self
organization process.
And, cause you've yet to rely on the
probability
that we generate these electrons and they
are distributed.
The separation of wavelength the
probability would be really negligible.
So how is this process taking place?
First we go back to the situation where we
have, is electron
B going through the undulator and we also have
an electron magnetic field.
There are complicating.
And, since the electron is in transverse
velocity and the electric field is
also transverse to the direction of
propagation, there is an energy exchange
which is proportional to the electric
field intensity, the
transverse velocity, and a cosine of this
face factor which is the relative.
phase of the electron velocity,

and radiation phase.
And, so, if this term remains constant
or changes by small amount during the time
we go
through the undulator, we can have a good
energy exchange.
This can only happen if you impose the
condition
that, that limitive of this quantity
should be 0.
And you know that 0.
is the trans, is that longitudinal
velocity and you evaluate this, you get
the condition that for this phase to be
constant, that the limitive to be 0.
The wavelengths of the radiation must be
equal to
the wavelengths of the spontaneous
radiation, emitted in the undulator.
So he can define, of course the velocity
depends on the energy.
We can define a resonant wavelengths, if
we this quantity doesn't change
and the resonant energy corresponding to
that so if
we are near to this energy we get a good
energy exchange since
these electrons have now a different
energy
depending on their position depending on
this phase.
When they propagate through exchanging
energy, it's
on the scale of the wavelengths again.
So when they propagate through the undulator
electron with the larger energy will
follow
this trajectory and the electrons with the
lower energy will be deviated more.
Okay so this generates a delay in the the
electron
dispectory scatter depending on the energy
change that they receive.
And because of this delay the electrons
tend
to bunch together on the scale of the
wavelengths.
Okay?
The electrons, they go faster.
Reach the electron that goes slower, and
they all tend to get together.
Now, if the electrons get together, you
have a larger branching factor.
And so you get more radiation.
So this process.
Is enhanced because you have more
radiation.
And so the process keeps repeating so you
go from 1 to 2 to
3 and back to 1, and you
get an exponential growth and exponential
instability.
As we will see more detail, this process
can be started from.
The initial noise in the longitudinal
distribution that we
must have otherwise, we wouldn't see any
spontaneous radiation.
Or it can be started from an external
electromagnetic field, like in the case of
Maybe's experiment.
But in all cases, you get this exponential
growth of the radiation.
And if I look at the longitudinal electron
distribution,
these are my electrons near the beginning
of the undulator.
If you have a random distribution.
As I move along, I start to see some
increased density.
This is all on the scale of one
wavelengths.
So, you have some partial branching by
the.
This point here, we have a pretty well off
micro bunch beam, all these
electrons are within, most of the
electrons
are within one tenths of the wavelengths.
So one tenths of an angstrom.
Okay?
So these two process go together, and the
process
stops at some point, and must stop of
course.
And we, we will see in more detail in a
moment.
So, this process can be characterized by
one parameter, what we call [INAUDIBLE]
parameter.
So it's got a lot of complicated elements
in it, but if you do the right theory.
You can reduce it to a universal form in
which everything
depends on one quantity only, which is
this FEL parameter row.
Which is the ratio of the rate of
parameter, with factor of four.
The beam plasma frequency which depends on
electron density and beam energy.
And the undulator frequency on
Omega U is 2 Pi C over lambda
So, given an electron beam, given this
energy
and density, you can evaluate this
quantity
and then you can evaluate RO , and
again length, the growth rate of the
power.
Is simply lambda U over 4 Pi RO
So, today's takes place when the
lesser radiation
power is a fraction draw of the beam
power,
which is the beam energy times the
beam current.
beam current.
And the saturation links is 10 times.
The gain length, the line width is
on the order of Ro so Ro tells everything, if
you know this parameter, or you evaluate it
and you know everything about
the system.
Typically, this Ro value is on
the order of 10 to the minus 3,10 to the -4.
So, If my period is
a few centimeters, I can get a gain length
on the order of some meters.
But the beam power, let's say that these
are all LCLS, the beam
energy let's say is 10GV, that's 10^10,
P current is 3 kAmps, so its 3.
Then to the 13, 30 terrawatt.
So out of that, I can get the fraction
Ro, so instead of 30 terrawatt I get 30
gigawatt.
And the length of the undulator this is
let's
say, one angstrom is about 5 meter I get.
Something in the order of 50 meters.
I need the long undulator, and then it's
all done.
If I want to evaluate the number of
photons that pair an electron.
They get the saturation is given by this quantity.
Is row times, is the photon intensity.
Photon beam intensity, which is...
This quantity ro q v.
Divided by the photon energy, 10 KV, 15
GV for energy.
0.1 aC, so it's about six ten to the eight
electrons.
And ro, ten to the minus 3.
I got 10 to the 12 electrons.
If I am looking at this container's
radiation based on what I told you before.
If let's say 10 to 9 electrons, I would
get 10 to the 7 photons.
And so in this case I get 10 to the 5,
more photons parameter which is nice.
Becomes a very efficient process, when we
use spontaneous radiation
we are really using these electrons in a
very poor way.
Because of each of electron, this
always assuming that you want coherant
photons.
For each electron, you get about one over,
100.
You get 10 to the 2 electrons to get 1
photon.
These are much more efficient process, so
we
are using these electrons in a much better
way.
'Kay?
This is the heart of the [LAUGH].
Questions?
We've been talking a lot.
Yes?
So, does that mean that.
So, do you have an electron bunch
going through undulator, and then it forms
micro-bunches, and
then you put it through another undulator,
and then use the light that comes from
that, because there are already
micro-bunches, or
do you end up with light where the
first part of the light is random, and the
second part of the pulse is.
>> You, you're.
You can use one undulator to start this
process and produce the micro-bunching,
and then take
this beam to another undulator where the
electrons
are already micro-bunched and will
generate the radiation.
This is a way, what we call, cell seeding,
we
yeah, you can combine these things
essentially you can think of an FEL
something which is always
built with one undulator you have
The first undulator corresponding to one
gain length
[COUGH]
sorry, generates spontaneous radiation.
Then you take this radiation and you input
it into the
rest of the undulator, and you amplify the
path that you, yeah.
And you can play around with this concept
in in many ways.
Of course, for all of this to work, you
have to satisfy this condition that we
were mentioning before.
You need a cold beam, so the energy's
spread should be smaller than Ro.
you must match the, electron free space
with the, photon free space.
And you must have some, thank you.
You must say something else.
[COUGH] As we all know, radiation
refracts.
So you generate radiation within the
electron beam
along the undulator but this tends to go.
Out of the beam.
And this can kill the process, unless you
satisfy the condition that the radiation
Rayleigh range is
longer than the gain length.
Which means that you generate more photons
that you lose by diffraction.
The, the Rayleigh range is defined in the
usual way, using the electron beam, that
they use.
So if you satisfy this, you are okay.
But now there is another
path to this process, this.
Instability takes place because the
electrons talk to each other and they're
saying that one electron generate an
electromagnetic field, generate a photon,
this photon travels faster, interacts with
another electron, so you start to
reach a correlation between electrons in
different parts of the electron bunch.
And this is critical to the growth to the
instability, as
if the electrons wouldn't talk to each
other, nothing would happen, okay?
We must talk, we must
listen to each other, essentially it's
like if you have people
thinking if, if singer cannot hear the
other one
you get noise out of it.
Okay?
But if they can listen to other people
when they sing, they get in tune.
Then you get beautiful music.
Now, here we have the same.
Situation and the photons tarvel faster than
the electrons, so they
can move forward and they can talk to
other electrons.
But only to an, a limited extent, because
the electron
velocities is smaller than the photon
velocity, but is still large.
So they can only interact within the
electrons
contained within a certain fraction of the
electron bunch.
And this fraction depends on the
difference
in velocity, between the light and the
electrons.
And this distance is called the
cooperation length.
It is the length which an electron
cooperates.
They talk to each other.
And, this cooperation length is again
defined by the same parameter rod.
The only thing you have to do is to
substitute on the little period with the
radiation wavelength.
Okay?
So, if I start from all this, electron
within one cooperation length.
Don't talk to electrons, reach out a few
corporation lengths away, and so,
since we are starting from noise, there is
only a limited connection
between the radiation generated by this
group of electrons, so what you get
spikes.
[COUGH] If you look again at this process,
and I
look at the spectrum, this is the spectrum
near the beginning.
Essentially
if I divide the beam in lengths
corresponding to one
wavelength, and I look at the noise within
that wavelength.
I guess some intensity proportional to the
local noise.
For this is a spontaneous radiation, if
you
analyze the spontaneous radiation, you get
something like this.
As you move along, in addition to these
microbunching, you have
this correlation between the radiation
emitted by the electrons within the same.
Cooperation lengths, or the next
cooperation lengths and then this tends to
be to change and instead of this very
noisy spectrum you have a few spikes.
The length of the spikes for LCLS, the
cooperation lengths is 40 nanometer.
The full length of a spike is about
two pi times this, so it's about 240.8
famtoseconds.
So depending on how long is my electron
bunch, I get a certain number of spikes.
The intensity in each spike fluctuates.
Lambda again.
But the number of spikes is a well defined
number, and
there is no correlation in phase or
amplitude between two spikes.
Because they cannot talk to each other.
So, this is another important part.
Now we can put all of this in mathematical
form.
And I think we can write the 
equation in
a universal form that does not contain
essentially any parameter.
That is you don't have the wavelengths,
you don't
have the beam energy, you don't have the
beam density.
You have only this quantity ro which
appears in theta and it
depends on the you see the changing phase
the changing energy.
The change in the electromagnetic field.
This is a complex quantity, this is
proportional
to the bunch factor as we have seen
before.
[COUGH] And we have, in these equations,
two variables.
1 is the longitudinal position along the
undulator,
the z bar measured in units of gain
length,
and the other one, Z1 is the position
within the bunch of an electron or the
photon.
Measure the units of the cooperation
lengths.
So once we introduce these two fundamental
lengths in
the process, you'll get this nice set of
equation
that you can solve and they apply to any
of the FEL of the wavelengths in
which it operates.
This is when the, and of course you have
to do
the three direction, but we have no time
for that today.
Now, then if I look again at these
equations, if
I have a at zero, alpha zero and banishing
zero, banishing
zero is a uniform electron beam which will
not generate any radiation at all.
Nothing changes, I stay there, so it is an
equilibrium point.
The next question is, is the equilibrium
point stable or unstable?
We can start at that by introducing
three collective variables, one is the
banshee, one
is this energy correlation, and one is the
field, which is, again, a corrective,
collective variable.
We can analyze this.
And, we can see that this, leads to an
unstable system.
So, we have these equilibrium pointers,
it's unstable so a little bit, of noise in
the bunching, or electric field,
electromagnetic field,
or energy distribution the system, start
to grow.
And, so we can build an FEL starting
from spontaneous emission, or from an
input radiation.
People are looking at an oscillator in
which you still start from spontaneous
radiation.
But then you filter it through Optical
Cavity.
The Optical Cavity for X-ray is, is not
easy, but people are looking at it.
So, all the system operating up to now
are this except for FERMI which
operates on seeding.
And flash to in Germany which we also
operates on seeding.
and we have done some formal seeding for
LCLS.
[SOUND] This is a spectrum due to this
spike
in behavior, so the FEL limited.
If I look at the if I go back to
this simplified form of equation in this
collective variable, so
I can start the behavior next to the equi,
[INAUDIBLE]
stable equilibrium point, but I can not
follow in detail.
I didn't get the saturation from this, but
if I analyze my previous equation, the one
for
each electron, I can integrate this
[INAUDIBLE] and non-linear, but it
can be done, then I can follow in detail
the system.
I see for instance that the field
altitude, this is in normalized
units, gross and then it oscillates around
value here.
I can follow the trajectory, I can see how
the bunching develops.
This is after Y undulator, because of the
interaction,
I get an energy modulation, and then this
energy modulation is absorbed in bunching.
At this point, I have a lot of bunching.
This is the distribution and phase and
energy.
Longitudinal phase-space.
But if I go after this point, these points
correspond to these points.
If I continue, these electrons continue to
rotate in this kind of potential web.
Formed by the, on the undulator, and the
radiation fields, and
you'll see that the bunching goes down,
and, in
fact, I lose intensity, and then the
process repeats.
There is a radio DC in this, so I can look
at all these details.
The beam energy, changes of course as I go
through this process, when I
arrive at this point, I'm getting away
from the [UNKNOWN] energy yeah [UNKNOWN]
>> [INAUDIBLE].
>> Okay time to go, time for lunch, okay I
will stop.
So An interesting point if I look at the
[UNKNOWN] number,
the number of photons per [UNKNOWN]
in volume.
Third generation light source, [UNKNOWN]
spontaneous radiation.
I get less than one photon.
Then to the ninth photons [UNKNOWN].
This was the first experimental proof of
[UNKNOWN] micron.
But, because the theory is universal, if
it [INAUDIBLE] technical details, but it's
true, it works.
These, again, a comparison of the these
LCLS, you'll see it today or tomorrow.
>> Tomorrow.
>> Big system kilometer long are the x-ray
[INAUDIBLE] this
is a summary of the characteristics pulse
energy up to a
few megajules line, reads then to the
minus 3 you can
look at all of these if you are in
interested in.
On the web, this is for the five other
x-rays being built, and you
have the same for the soft x-ray, the
seeded and non-seeded.
These are measurement of the [INAUDIBLE]
creative properties, pretty good.
So you have good transfer clearance.
We can use these for refraction imaging.
This is what we were discussing before,
what you suggested.
You take one of the liter working in
SASS and you select certain boundaries
with the crystal.
And then you seed these things [INAUDIBLE]
you destroy the bunching here.
And you'll see this signaling to your
electron
beam, and you'll get, instead of the
noises
spectrum that we showed before of any nice
line, these are [UNKNOWN] has been done
here.
It works.
Was proposed initially dizzy.
We can also generate very short bunches
with
one spike, and that sort of [INAUDIBLE]
limited.
We can extend the cooperation length by
playing around
with the electrons and photons and get
better coherence.
Laser [INAUDIBLE]
on [INAUDIBLE]
beam, Once we have the micro bunching, we
can avoid the saturation
by changing, that's due to changing the
electron beam energy.
But it would change the magnetic field, we
can maintain the
rest of its condition and we can get to
the terawatt.
This is a demonstration by adjusting the
magnetic
field after saturation you get a really
nice line.
In these experiment, in maximum power is a
hundred gigawatts.
And more now.
You can do two colors in many ways.
And some of these are being used now in
experiments
that are LCLS which are going on today, I
believe.
For a [INAUDIBLE]
biology,
particularly using this you inject two
electron bunches separated by a
small distance, and you do self seeding,
and you get two very
nice narrow lines separated and you can
get mad experiments.
And you can do a lot of nice experiment.
These are two examples.
This is the three panel [INAUDIBLE]
and this is looking at
normal modes in a gall manel crystal and
many more experiments, okay thank you.
>> Thank you very much.
[SOUND]
>> For more, please visit us at
stanford.edu.
