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VARIABLE ATMOSPHERE EFFECTS ON HIGH ENERGY LASER PROPAGATION
R. Ruquist
To cite this version:
R. Ruquist. VARIABLE ATMOSPHERE EFFECTS ON HIGH ENERGY LASER PROPAGATION.
Journal de Physique Colloques, 1980, 41 (C9), pp.C9-121-C9-128. �10.1051/jphyscol:1980917�. �jpa-
00220571�
JOURNAL DE PHYSIQUE CoZZoque C9, suppZ6ment au nO1l, Tome 41, novembre 1980, page C9-121
V A R I A B L E ATMOSPHERE EFFECTS ON H I G H ENERGY-LASER PROPAGATION
Avco Everett Research Laboratory, Inc. Everett, Massachusetts, U.S.A.
Abstract.- Propagation of high energy laser beams to space has previously been evaluated on the basis of constant, seasonally averaged standard atmospheres, time constant levels of turbulence with the appropriate altitude profile, and time constant winds in direction and velocity, independent of alti- tude. In actually, atmospheric conditions are highly variable resulting in a large spread in propa- gation performance as a function of time. The purpose of this paper is to develop a methodology for determining the propagation performance on an annual probability basis, and to give an example of the use of this methodology. Particular emphasis is addressed to the statistical modeling of thermal blooming, a nonlinear absorption phenomenon that limits the maximum amount of propagated laser power.
Introduction
In order to estimate the spread in propagation performance within a temporal variable atmosphere, we modified the AERL standard atmosphere laser propagation code to calculate the aperture optical gain from temporal records of temperature, dew- point,wind speed, wind direction and atmospheric turbulence. In this paper we present calculations of aperture optical gain based on hourly vertical profile measurements of the above meteorological variables and a diurnal average of atinospheric tur- bulence seeing data all taken at a thite Sands, New Mexico mountain location. Calculations of opti- cal gain are made for each hourly set of data and averaged over monthly and longer periods. The results are presented as cumulative probability distributions so as to reveal the spread in propa- gation performance.
For very large aperture power, the dominant con- tributor to the statistical spread in performance
. .
is variation in wind direction through its in- fluence on thermal blooming. When wind and slew are opposite, the beam is cleared of heated air with a minimum of pulses of a numblr known as the
closely aligned with slew, the number of pulses to clear the beam increases as the cosecant of the rind/
slew angle. Theref ore, wind directed laser slewing will maximize thermal blooming and wind-opposite
slews will minimize thermal blooming. In this paper, the dependence of propagation ~erformance on the orienta- tion of slew to wind direction is examined. In
addition, we present calculations illustrating the dependence of propagation performance on tilt cor- rections and adaptive optics for turbulence and thermal blooming compensation. Emphasis is pl.lced on assessment of "stagnation zone" blooming effects and,optical corrections thereof. Comparisons are made to previous calculations using constant (stan- dard atmospheric coding and favorable wind directions.
Xon-Coplanar Thermal Blooming Modeling
Previous investigations of "stagnation zones" in . propagating laser beams have concentrated on co- planar thermal blooming where laser slew and winds are codirectional. As a result, the stagnation effect was often found to be divergent. Four-di- mensional codes2 were required to treat the pkoblem accurately and results suggested that in
"overlap number". But as the wind becomes more
T+settr~~
- ~ - t + r ~ i i - i S e ~ ~ - A-,.-~G Massachusetts, U.S.A.Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980917
C9-122 JOURNAL DE PHYSIQUE
the limit of large pulse number the beam temperature Any increases in overlap number due to non-co- reached a steady-state at the stagnation point due to planarity or variable wind speed can be effectively stagnation point motion. The coplanar analysis of the modeled as increases in average power in the co-
"stagnation zone" region neglects an important 3 if not planar thermal blooming model. .Therefore, ef fee- dominant, heat removal mechanism; namely, the out-of- tive increases in the number of overlaps t~ clear
lane
component wind velocity which clears heated air a beam of heated air in the non-coplanar model can more quickly than any other mechanism (except when also be modeled by scaling average power in the wind and slew are so aligned that thermal blooming co-planar model.has severely limiited optical gain). Comparison of the out-of-plane wind component mechanism to other heat removal mechanisms such as stagnation point motion that li~its the effect of tllermal blooming is beyond the scope of this paper. Instead, we assume that a steady-state thermal blooming model
based on atmospheric clearing winds is a good 0
-- -
- - .-.approximation everywhere except in severe stagnatioll - .
blooming where propagation is very poor.
Our modeling is based on scaling relationships
8 = ANGLE BETWEEN ANTI
-
SLEWAND WIND DIRECTIONS added to existing algorithms in a constant coplana:~ - .
Fi4. 1 Heuristic NOn-Goplanar Model atmosphere propagation code. We note that the
We first develop the power scaling relationship thermal blooming distortion number for repetitively,
from heuristic considerations. Figure 1 indicates pulsed propagation to space is proportional to the
the number of pulses required for the wind to clear overlap number, i.e., the number of pulses required
a circular beam from a circular aperture. There- to clear the beam of tteated air at the aperture.
fore, as the wind/slew angle approaches 180°, the ak<P>hs akj hs
N =
---
=-
D JoVwDu JoU No
where N =
- D-y
is the overlap number, h =W
scale height for atmospheric absorption, and u =
distortion number or scaled average power in the thermal blooming algorithm approaches infinity.
r v /
I 0 APPROXIMATION N* VI
cosine of the zenith angle.
.
X 10 5 4 m / , 2 n1. PULSE<P> = E ' PRF is the average power NORMALIZED O Z L 8 m l s
RMS PHASE FLUCTUATIONS
j
*
E/D' is the transmitted fluenceand Vu(cm/s) is the wind speed directed opposite the N o laser slew ws(rad/s); k = 2n/X is the laser' propa-
gationconstarit, a is the beam extinction at the
aperture and Jo is proportional to absolute tempera- 8 (DEGREES) TRANVERSE WlNOlSLEW ANGLE
ture of the atmosphere and is approximately 1300
rig. 2 Steady State Thermal Blooming with Stagnatloq joulcs/cc at 300~1:.
In order to improve on the above heuristic modeling, we also made similar calculations using a repetitively-pulsed propagation code based on the Born approximation. A summary of these results appears in Figure 2 where we'plot phase fluctuations due to thermal blooming as a function of the windlslew angle 8. The magnitude of the phase fluctuations relative to its magnitude at 9 = 0 defines a power scaling relationship similar to the above heuristic one. We see from compari- son of the asymptotic l/sin@ dependence (repre- sented by dashed line) and the Born approximation calculations that distortion number is increased by a factor of 2 between 8 = s/2 (wind at right angles to slew) and varies closely to I/sin8 be- yond n / 2 except for saturation effects due to the propagation of a finite number of pulses. Clearly at e = s, as the number of transmitted pulses in- creases the thermal distortion is likewise in- creasing and the I/sin9 curve is consistent with these results. As the Born approximation calcula- tions are more complete than the above heuristic analysis, the non-coplanar thermal blooming scaling relationship for power becomes
<P> -((I t sine), 19
1
< n/2"0' 2/sin8
, e (
> r / 2The scaling is accomplished by inserting the above relationship in the appropriate al~orithm in the standard atmosphere code. For atmospheric turbu- lence, we use a diurnal variation of ro (500 nm) based on measurements at the White Sands mountain site- averaged over several months.
i I IL
O OO 8 I2 I6 2 0 2 4
T I M E OF D e Y ( H O U R )
12 1
REF WALTERS. A S L
-
-W a -
- W UJ
Fig. 3 Diurnal Model for Atmospheric Seeing
w
% 2 a
U
The diurnal variation of ro is shown in Figure 3.
Characterization of variable atmospheric winds is presented as cumulative probability distributions of the various meteorological parameters.
Figure 4 indicates the distribution of horizontal
A . 0 5 , ~ r n
2 m APERTURE HEIGHT
-
WHITE SANDS MOUNTAIN SITE - MAY-DEC 1978
- -,
wind speeds made at a White Sands mountain by Atmospheric Sciences Laboratory for a single month in 1977 and for seven months in 1177 (un-
published). The distribution has a mean of 5 m/s (parameter used in standard calculations). The
In
- . 5 0
HOllRl II DATA
> W H l T E L A N D S M O U N T I ~ N 51TE REF ASL
V w - W I N D S P E E D I m l s 1
Fig. 4 Distribution of Wind Speeds
C9- 124 JOURNAL DE PHYSIQUE
power scaling relationship for wind speeds other than 5 m/s is again based on the overlap number which is inversely proportional to wind speed and
therefore the power used in the thermal blooming algorithm is inversely proportional to the wind speed.
V)
D J A N
-
JUNE 1977Fig. 5 Distri'onti~. nf_' Wind Directions
The distribution of wind directions at t-he mountain locale are plotted in Figures 5 and 6 for seven rno~lti~s and one month of hourly readings.
The winds are prevailing 180' for 60% of the t h e . As mentioned above, stagnation effects will domi- nate when the laser slews at this angle. There- fore, we have chosen two slew angles, 22O and 158' to represent typical but not worst case, examples of thermal blooming with and without
0 90 160 2 7 0
B - W I N D SOURCE DIRECTION ANGLE
Fig. 6 Distribution of Wlnd Direetions
stagnation effects. These angles are indicated in Figures 5 and 6.
Table I. Parameter Space
Atmospheric condition: Mid-latitude summer and winter or meteorological variables, cloud-free.
Installation altitude: 2.5 km.
Atmospheric turbulence. Average visible lateral coherence length ro (500 nm) specified as a diurnal variation from averages of 112 year data.
Long-term atmospheric turbulence.
Tilt removal for atmospheric turbulence.
Adaptive optics to remove atmospheric turbulence.
Isoplanatic patch limitations for adaptive optics phase correction for atmospheric turbulence.
Pointing and Tracking Jitter: Standard deviation per axis = 0.5 pr.
Linear Extinction Water vapor
Bleaching of C02 by CO laser pulses Tuning of C02 cavity 2
Thermal Blooming
No aperture corrections
Thermal blooming phase corrections Beam Quality = 1.0
Atmospheric Transmission
Temperature and dew point temperature essen- tially determine atmospheric extinction and atmospheric transmission. We summarize the dis- tributions of these parameters by presenting cumulative probability distributions of vertical transmission through the atmosphere. For altitude dependence, we have used monthly average altitude profiles for temperature and dew point tempera- ture from measurements taken over Albuquerque, New Mexico in 1975. These profiles are plotted in Figure 7. In order to incorporate them in our modeling, we note that the profiles are very similar except for their ground level value.
That is, the dew point temperature falls 7O/km on the average for several kilometers. Likewise, the temperature increases 3O/km of 112 km and then falls 7O/km above 112 km.
These profiles have been integrated to obtain are then accumulated into cumulative probability the vertical transmission coefficiency distributions as shown in Figures 8 and 9. Fore-
sight allows us to conclude that these distribu- tions have a relatively narrow statistical spread
compared to the overall propagation performancp.
Therefore, temperature variations are not the dominant contributor of system effectivenessto the statistical spread.
TRANSMISSION To =,-q.dh COEFFICIENT a
0
DEW POINT I ' C I , TEMPFRATURE I'C)
VERTICAL PROPAGATION
Fig. 7 !Rawinsonde Data
-
Average Monthly 'Values, Albuquerque, 1975for each hourly measurement of temperature and CUMULATIVE PROBABILITY T >Tb
relative humidity taken at the White Sands
Fig. 9 June Statistical Variation of Vertical Transmission Coefficient
mountain location. The calculations were per-
formed for X = 10.6
urn
The 10.6 um calculations Propagation Performancewere performed with and without line tuning. We shall use the aperture optical gain G defined With line tuning the transmitted wavelength is below as a measure of system effectiveness.
0
shifted 12A away from line center of the 1-atm C02 absorption line. As a result, the integrated vertical CO extinction is reduced by an order of
2 where $ is the peak focal flux at range R 'delivered
by a laser of average power P. The calculation is magnitude. All of the above calculations from
January through July 1977 and for June of 1977 performed for each hour of data and proceeds by a determination of the range or altitude R for which
$/P = 2 x 10-~/cm~ can be achieved on an orbiting
V E R T I C A L TRANSMISSION COEFFICIENT
7
*
- -eJ--
a dh receiver passing over the location at 22O and 158O.Thus, each calculation involves an iteration because the laser slew velocity, which is a f,unction of Rr enter into the determination of the variance og due to thermal blooming.
The calculations for propagation performance are performed with three levels of phase compensa- tion algorithms for atmospheric turbulence:
JAN -JULY 1977
WHITE SANDS MOUNTAIN SITE VERTICAL PROPAGATION
.Z
0
0 2 4 6 0 10
CUMULATIVE PROBABILITY T >To
Fig. 8 Semi-Annual statistical Variation of Vertical Transmission Coefficient
JOURNAL DE PHYSIQUE
1. Uncorrected; long-term turbulence 2. Tilt corrections, short-term turbulence 3. Adaptive optic corrections for atmos-
pheric turbulence (perfect: infinite number of adapters.); isoplanatic effects.
Even with perfect adaptiw optics, turbulence corrections are not exact because of a combina- tion of lead time to sample the turbulence and isoplanatic effects. That is, by the time the high energy pulse is transmitted, the laser beam has slewed away from the turbulence sampled.
and slew are largely opposlte and thermal blooming is not severe. A representative sample of calculations without compensation for thermal blooming are shown on Figure 10. In each of these plots the top curve corresponds to perfect adaptive optics; the middle curve corresponds to tilt cor- rections and the bottom curve is uncorrected for atmospheric turbulence. Separate plots are pre- sented for 10.6 urn with .and without cavity tuning, both for hourly data taken in June 1977 for 22' and 158' slew angles, and hourly data January to July 1977 for the 22O slew angle.
*o'Z , , , ,
JUNE 1977 J U N E 1977
Some general conclusions may be drawn from com-
JUNE 1977
I
10"= -
IOIllm. LlHE l U N l N G 22. SLEW
to' ' ' '
0 0 2 0 4 0 6 0 0 10 0 2 0 . 0 6 0 8 I 9 C U M U L A T I V E P I O B A O I L J T Y G I G O
Fig. 10 Comparisons of the Statistical Varia- tion of Optical Gain. Each plot con- tains three levels of phase compensa- tion for atmospheric turbulence, but no thermal blooming compensation.
Top curve: perfect adaptive optics Middle curve': tilt corrections only Bottom curve: no corrections
System effectiveness calculations have only been performed at h = 10.6 um. They were made under a variety of conditions including phase compensation for thermal bloomi-ng for two laser slew directions: 22', for which thermal
parisons of these plots. Line tuning increases system effectiveness overall by a factor of two but has little effect on the spread of the distribution.
The spread of the distribution is primarily due to the spread in wind directions, and secondarily on the spread in atmospheric temperatures. The rela- tive lack of thermal blooining effects are evident in the 158' slew angle calculations. Here the diurnal variations of atmospheric turbulence are evident, and the spread in the uncorrected-for- turbulence curve is almost as great as at 22' slew angle. This suggests a need for at least tilt corrections to obtain good optical gain for 80% of the time, regardless of wind-slew angle.
The low values of optical gain without corrections are due to calculations corresponding to data taken in the middle of the day when turbulence is most severe. One general conclusion is that at
at least at 10.6 um, tilt corrections alone are almost as effective as perfect adaptive optics.
blooming is severe; and 158O for which winds
I n o r d e r t o i l l u s t r a t e thermal blooming compensation e f f e c t s , on F i g u r e s 11 we p10.t t h r e e p o i n t s from t h e cumulative p r o b a b i l i t y d i s t r i b u t i o n ( t h e 20%, 50% and 80%) a s a f u n c t i o n of t h e power improvement f a c t o r which r e s u l t s from blooming compensation. We p l o t c a l - c u l a t i o n s w i t h o u t tilt c o r r e c t i o n s and compare c a l c u l a - t i o n s based on h o u r l y d a t a r e a d i n g s t o s t a n d a r d c a l c u l a - t i o n s based on c o n s t a n t , s t a n d a r d atmospheres. The
upper and lower bounds t o t h e c r o s s hatched a r e a a r e m i d - l a t i t u d e w i n t e r and m i d - l a t i t u d e summer s t a n d a r d
STANOARO ATMOSPHERE PREDICTION
I
+
NO THERMAL CORRECTIONU
-
THERMAL CORRECTIONHOURLY DATA JAN-JULY 1977
0 WHITE SANDS MOUNTAIN SITE
22. SLEW
. lO.6pm L I N E CENTER NO TURBULENCE CORRECTIONS
0 2 8 10
POWER FACTOR DUE TO THERMAL CORRECTIONS Fig. 11 I l l u s t r a t i o n of t h e P o t e n t i a l
f o r Blooming Compensation
atmospheres u s i n g t h e nominal 5 m / s wind, corresponding t o approximately t h e mean wind speed from F i g u r e 4 , and with t h e wind o p p o s i t e t o t h e d i r e c t i o n of l a s e r , which thereby minimizes thermal blooming e f f e c t s .
The comparison of t h e s t a n d a r d c a l c u l a t i o n of nomi- nal. g a i n s t a t i s t i c s t o c a l c u l a t i o n s of g a i n based on d a t a i s remarkable. Without thermal blooming c o r r e c -
t i o n s ( i . e . , f a c t o r = 1.0) t h e nominal g a i n
i a
achieved 20% o r l e s s of t h e time. The g a i n achieyed.
f o r 80% of t h e time is a s nuch a s a n o r d e r of magni*
t u d e l e s s t h a n t h e nominal g a i n c a l c u l a t e d by t h e s t a n d a r d MRL Code, The dominant r e a s o n f o r such
l a r g e d i s c r e p a n c i e s i s t h e assumption t h a t t h e l a s e r slew d i r e c t i o n i s o p p o s i t e t h e d i r e c t i o n of atmos- p h e r i c winds i n t h e nominal c a l c u l a t i o n s .
Use of phase compensation f o r thermal blooming r e - s t o r e s system g a i n t o t h e l e v e l of t h e nominal c a l c u l a - t i o n s i n most c a s e s . For uncorrected ( f o r t u r b u l e n c e ) beam p r o p a g a t i o n , t h e nominal c a l c u l a t i o n of g a i n i s modest, and i n t h e mean, t h e g a i n i s r e s t o r e d by a 50%
thermal blooming c o r r e c t i o n . That i s , a thermal blooming c o r r e c t i o n t h a t p r o v i d e s 50% e x t r a power t r a n s m i s s i o n f o r t h e same thermal blooming beam spread
a n g l e n r e s t o r e s t h e mean g a i n t o above t h e MLS gain.
B
With t i l t co;rections f o r t u r b u l e n c e , t h e nominal g a i n i s much h i g h e r a f a c t o r of 10 thermal blooming power c o r r e c t i o n i s r e q u i r e d t o r e s t o r e t h e mean g a i n t o nominal l e v e l s . However, i n both t i l t c o r r e c t e d and ' u n c o r r e c t e d p r o p a g a t i o n , t h e spread i n c a l c u l a t e d
system g a i n i s only s l i g h t l y a f f e c t e d by phase com- p e n s a t i o n . For example, t h e uncorrected 80% g a i n remains f a r below t h e nominal g a i n because of high daytime l e v e l s of t u r b u l e n c e .
Conclusions
This paper p r e s e n t s modeling t o o b t a i n e s t i m a t e s of high energy l a s e r p r o p a g a t i o n e f f e c t i v e n e s s f o r , i r r a d i a n c e of o r b e t i n g r e c e i v e r s on an annual proba- b i l i t y b a s i s . I n p a r t i c u l a r , i t i n d i c a t e s t h e i m - p o r t a n c e of thermal blooming modeling t h a t i n c l u d e s dependence on wind d i r e c t i o n coupled t o measure-
m e r t s of t h e s t a t i s t i c a l v a r i a t i o n of wind d i r e c t i o n and ~ d n d i n t e n s t r y . Xn p a r t i c u l a r , com?arisons of + t i c a l g a i n
for
a FJ"nite Sands m o u n t a h l o c a t i o n i n - d i c a t e t h e e f f e c t s of t h e s t a t i s t i c s of wlnd d i r e c - t i o n s on propagation performance e f f e c t i v e n e s s . For t h e p a r t i c u l a r c a s e s considered h e r e , where t h e prc- y a i l % n g winds a r e c l o s e t o t h e p l a n e of ciie s a t e l l i t et r a j e c t o r i e s , t h e n a 50% l o s s i n c a p a b t l i t y may occur.
That i s , 50% af t h e time t h e o r b i t a l t r a j e c t o r y w i l l b e f r o m s o u t h t o n o r t h and thermal blooming w i l l
c9-128 JOURNAL DE PHYSIQUE
seriously degrade system effectiveness. However, phqse cornpensatton blooming can restore system capability to nominal levels regardless of traL j ectorvc
Acknowledgements
This work was supported by the AERJ.. Independent Research and Development Program. The suggestion of fine tuning of the cavity was made by
Dr. Jack Daugherty, and the initial calculations were performed by D.H. Douglas-Hamilton, both of AERL. Turbulence algorithms and trajectory coding were developed by Dr. G. Sutton of AERL. Greater detail of the propagation algorithms in the standard AERL Code may be found in their papers. 596
References
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2. Fleck, Jr., J.C., Morris, J.R., and Feit, M.D.,
"Time-Dependent Propagation of High Energy Laser Beams Through the Atmosphere," Applied Physics, Vol. 10, pgs. 129-160 (1976).
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Paper No. 77-655, AIAA Tenth Fluid and Plasma- Dynamics Conference, Albuquerque, New Mexico
(June 1977).
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