When q is a constant, then it is a geometric series. The sum of n members of the geometric
series is:
(12.5)
12.3.4 Limitation of reflection number
If the reflector is moved away, the maximum number of reflections, n, is limited by cell
size, l, because the wavelength, , is increased and that cannot be more than the cell size.
This limit is:
(12.6)
where l is the cell width [m] and
0
is the initial wavelength [m].
If the reflector is moved forward to another position the wavelength is reduced, but it
cannot be less than the wavelength of X-rays because the material transmits the X-rays
(the material lessens the reflective capability).
This limit is about
min
10 nm. The maximum number of brake reflections is:
(12.7)
12.3.5 Coefficient of efficiency
The efficiency coefficient, , may be computed using the equation:
(12.8)
12.3.6 Focusing the beam
If the lens used in focused at a range S
1
, the distance, S, without ray divergence is
(Fig. 12.2(b)):
(12.9)
where D is the diameter of the lens or mirror [m].This distance is equal to the lens focus
distance for the case in Fig. 12.2(b) (S
1
S). In the case Fig. 12.2(c) (transfer over very
long distance), the optimal focus distance is S
2
2S
1
.
S
D
D
S
DD
2u
u
p
lp
ll
,
2
,
4
0.443 ,
22
h TV N/.
0
n
v
ln( / )
2
.
0
ll
min
n
l
v
ln( / )
2
,
0
l
T
N
c
q
q
If n then T
N
cq
q
n
2
1
1
.,
2
1
1
,1.
00
232
Ch12-I044731.qxd 3/1/06 11:30 AM Page 232
Get Non-Rocket Space Launch and Flight now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
