due to the oscillating charge in the antenna along this line one does not observe any acceleration...
TRANSCRIPT
due to the oscillating charge in the antenna
Along this line onedoes not observeany acceleration
Radiation from a dipole-antenna
R
charge ; ( , ) ( / )rad radE q E R t observed acceleration t R c
20
1 1( , ) ( / ) ;
4rad
eE R t acc t R c
R c
To get the dimension right !
Electromagnetic radiation( / )
0
( / )0
mass acceleration force=charge field
[ ] ( / ) [ ]
[ ]
[ ] ( )
i t R cin
i t i c R
i kRin
m acc e E t R c e E e
e E e e
e E t e
0
25
0 20
( ) ;
( )
1 2.82 10
4
i kRrad
in
E t er
E t R
er Ang
mc
Here one observes the full acceleration,but delayed in time by R/c !
1( )radE R
R
Guess that
2 22 2
1 14radE energy density radiated energy R
R R
20
2
2
m/sec Force = Energy
1( , )
4
OK(m/sec)
rad
e acce E R t
R c
2
Polarisation
P=cos2(ψ)
P=1
Interference (mathematical)
z
r
rk zkz
in
2
k’ Q
rk ' outrQrkk )' ( res
0. . (1 )isc ampl r e Q r
0. . ( ) isc ampl r e d Q rr r
Number density
0. . ji
j
sc ampl r e Q r
many
wavecrest
k1
2
as drawn #2 is behind #1 for ”in”
but ahead for ”out” , therefore ” – ”
Phase
0 .
1,2 … many
The dream experiment
2 *2 1 2 2 2 2;i iA f e f e I A A 1Q r Q r
2 2
1 2 1 2
2 1 2 1 2
( ) ( )2 21 2 1 2 1 2
{ } { }
i i i i
i i
I f e f e f e f e
f f f f e f f e
1 1Q r Q r Q r Q r
Q r r Q r r
2 2 122 1 2 1 2.
12
sin( )2
orient average
Q rI f f f f
Q r
2
.
sin( )2 i j
i i jorient averagei i j i j
Q rI f f f
Q r
1,2 … many
DetectorViewingField
Detector
X-ray beam
Kr
Gas cell
sin2
)(2sin
1 2
kQ
QfIntensity
Measuring atomic and molecular formfactors from gas scattering
j
ijmol
ielatom
jeff
def
rQ
rQ rr)(
a=[15.2354 6.70060 4.35910 2.96230]; b=[3.0669 0.241200 10.7805 61.4135];c=1.71890; % Ga
a=[16.6723 6.0710 3.4313 4.27790];b=[2.63450 0.2647 12.9479 47.7972];c=2.531; % As
24( / 4 )0
1
( ) jb Q
j jj
f Q a e c
1cos 2 ( )
sin sin( )
2 2sin
Qri x
i Q r
x Qriorientationalaverage
Qr e dxe d d Qr
eQrd d
Q r
Unit sphere
d
d
r
Q
iorientationalaverage
e Q r
r
sinsind
sind d d
Fourier transform of a Gaussian
Fourier transform : ( ) ( ) i q xF q f x e dx
2 2
( ) a xf x Ae
2 2/(4 )( ) q aAF q e
a
2 2 2 2/ 2 / 21or with ( ) ; ( )
2x qf x e F q e
( ) ( ) when 0Gaussian x x
( ) ( ) (0) f x x dx f
F.T. 1 (delocalize( ) ( )
localized
d in )
in
Gaussi qan x x
x
Convolution of 2 Gaussians
2 2 2 2( ) / 211 1 2/ 2
1( )x xx
h x e e dx
2 2 2 2 2 2
1 2/ 2 / 2 / 2( ) q q qH q e e e
i.e. h(x) is also Gaussian with 2 2 21 2
Side View
Top ViewRing wave (2D) orSpherical wave (3D)
2 23D : 4 independent of i k re
A r rr
Energy density Surface area
locally a plane wave iAe k r
Aperture d Almost planewave when
d
Perfect planewave
k’
k
A point scatterer in the beam
i kReA
R
Spherical wave
2Flux : c Intensity Flux Area scattered in
thru
dI
d
22
2
2
2
i kR i kR Ac e e R
R
c A
dA
d
Defines thescatteringcross section1c
Area is
2R
scattering length
scattI i k x
in e
2LL=(N+1)(
2LL=NNo real beam is perfectly monochromatic
From the 2 equations, derive
21
2LL
the longitudinal coherence length
P(
wavelength band
No real beam is perfectly collimated
P(
D
2 TL
LT
Hereand B beams in phase
A and B out-of-phase
show from the figure that
2T
RL
D
With R being the distance from to
source observation point
A
B The transversecoherence length
Absorption
zeIzI
dzzIdI
0)(
)(
) ,number atomic( Z
34 1
) ,(
ZZ
The experimental setup
X-rays
Sample
Rotation
Scintillator
20m
CCD
< 2 mdeg
E = 8-27 keV
0.7 x 0.7 mm
Tomography
• Study the bulk structures, 3D
• Nondestructive• Small
lengthscales (350 nm)
Fra http://www.unge-forskere.dk/
Galathea III
Single slice
100 microns
Compton Scattering
3
'1 (1 cos )
'
3.86 10
C
C
k
Åmc
Energy and momentum conservation