High power pulsed lasers - Springer Link

Journal of Fusion Energy, Vol. 2, No. 1, 1982

Review Paper

High Power Pulsed Lasers J. F. Holzrichter, ~ D. Eimerl, 1 E. V. George, ~ J. B. Trenholme, 1 W. W. Silnmons, ~ and J. T. Hunt ~

Received November 16, 1981

Pulsed high power lasers can deliver sufficient energy on inertial fusion time scales (0.1-10 ns) to heat and compress DT fuel to fusion reaction conditions. Several laser systems have been examined for application to the fusion problem. Examples are Nd : glass, CO2, KrF, and I2, etc. A great deal of developmental effort has been applied to the Nd:glass laser and the CO2 gas laser systems. These systems now deliver >104 J and > 2 0 • 1012 W to inertial fusion targets. The Nova Nd:glass laser is being constructed to provide > 200 kJ and > 200• 1012 W of 1 /~m radiation for fusion experimentation in the mid-1980s. For inertial fusion target gain, > 100 times the laser input, it is expected that the laser must deliver ~ 3-5 MJ of energy on the 10-20 ns time scale. This paper reviews the developments in laser technology and outlines approaches to construction of a 3-5 MJ driver. KEY WORDS: Laser; fusion driver; laser fusion; inertial fusion; h/gh power lasers.

1. I N T R O D U C T I O N The fusion reaction provides virtually a limitless source of energy because its fuel is the vast amount of deuterium contained in the world's water supply. The potential benefit of this energy source has motivated thousands of scientists, ourselves included, to search for methods to contain the fusion reaction in a controlled fashion. The most reactive fusion fuel, deuterium (D) plus tritium (T), must be heated to 10 keV and confined with a density-time product ~ - greater than 1014 i o n s / c m 3 for efficient burn of the fuel to occur. (1'2) The magnetic fusion process uses magnetic fields to hold D and T ions in close proximity (density of ~1014 i o n s / c m 3) for ~'~10 s, satisfying Lawson's criteria~3) of ~l"r>1014, in this case ~-=1015. The magnetically contained plasma is heated by neutral ion beams, ohmic current, or rf fields to the required 10 keV temperatures. For inertial fusion, a pellet of ILawrence Livermore National Laboratory, University of California, Livermore, Calif. 94550.

D T fuel is first compressed to high density (n = 3 • 10 25 particles/cm 3) by ablating the outer surface layers away at high velocities.(4'5) The ablation pressure compresses the fuel and heats the fuel to - 1 0 keV. When the fuel begins to ignite, energetic a particles from the D-T reactions are stopped in the compressed fuel. This additional deposition of energy causes the temperature and burn rate to increase, leading to fuel burn-up in ~ 30• 10 -lz s, before the ions can expand and decompress. In this process, the ~" = 1015, and T~on> 10 keV. For the inertial fusion target to reach the necessary ignition conditions, the driver must provide sufficient energy, presently estimated to be 3-5 MJ, on a time scale of 10-20 ns. It is necessary that the focused beam attain a sufficient power density on target to provide sufficient ablation pressure to compress and heat the fuel. Finally, the interaction between the driver beams and the target must occur in such a way that the implosion dynamics are optimized. Preheat of the directly driven target's shells and fuel due to energetic electrons or ions and nonspherical compression caused by nonuniform beam 0164-0313/82/0200-0005$03.00/0 9 1982PlenumPublishingCorporation

6

energy deposition can raise the energy required for ignition and high gain by several factors of 10. The experimental programs have shown that we are able to control both of these problem areas. The main objective of present inertial fusion research is to determine the minimum driver energy and power necessary to ignite the fuel droplet and cause it to burn efficiently. Both lasers and ion beams are being developed to produce the necessary ignition conditions. In this paper, we review the technology and present the status of fusion lasers. 1.1. The Laser: Origin

The laser, as we now use it, was first described by A. L. Schawlow and C. H. Townes in 1958.(6) It was experimentally demonstrated in 1961 by T. Maimen. (7) In the laser, coherent light is generated, amplified and propagated at fluences below damaging levels. This light can then be focused to very high intensities. Using focused laser beams, experimenters began to study matter under conditions of pressure, temperature, and density that had been attainable only under much more difficult experimental conditions. In the early 1960s it was realized that matter could be heated to temperatures high enough to induce fusion reactions. (s'9) Between 1960 and 1970, many laser systems were discovered, and most of the basic ideas associated with laser amplification, laser light propagation, and limits on beam intensification were published. Work on lasers specifically designed for plasma research began in the mid 1960s. Excellent references to the work of this period are given in ref. 10. Glass lasers specific for plasma and fusion applications were developed by the Compagnie General D'Electricite (Marcoussis, France), at the Lebedev Institute (Moscow, Russia), at Sandia Laboratories (Albuquerque, N.Mex.), at the Naval Research Laboratory (Washington, D.C.), at the University of Rochester (Rochester, N.Y.), and at the Lawrence Livermore Laboratory (Livermore, Calif.). The power levels of the first systems were modest, about 0.01 TW (1 TW = 1012 W). In the early 1970s, it was proposed that energy producing nuclear fusion was feasible(4'1~) using the inertial confinement fusion approach. Several institutions started programs with the purpose of developing research laser systems for target irradiation at the - 1 0 kJ, 10 TW level~ (see Fig. 1). Experimental work began in earnest with demonstrations of target

Holzrichter et al.

compression and fusion reactions occurring first at KMS Fusion, Inc., (13) and soon after at the Lawrence Livermore National Laboratory (14) and elsewhere. (12) During the period from 1970 to the present, a wide variety of laser plasma interaction experiments and implosion experiments were carried out. 02'15-1v) The most recent of the imposion experiments were carried out with ~ 10 kJ of energy delivered to a target in less than 1 ns, resulting in fuel compression of 100 • DT density. Or) Physics experimenti were conducted at many institutions, using lasers with wavelengths ranging from 0.25 to 10/~m. They have demonstrated (18) that with irradiation wavelengths less than 0.5/~m and at intensities of ~3X1014 W / c m 2, the laser plasma interaction becomes nearly classical and the absorption is dominated by inverse bremsstrahlung. Most importantly, the undesirable hot electron component of the electron distribution is greatly reduced for wavelengths less than 0.5 /zm. These results lead to the projected target performance as a function of input energy shown in Fig. 2. The region of the curve at 0.1-0.2 MJ of laser energy is where we expect target ignition to begin. Ignition occurs when the target generates significant self-heating from the aparticle deposition. With 3-5 MJ of driver energy, we expect target gains of ~ 100 to occur. These high gain experiments will demonstrate the scientific feasibility of inertial confinement fusion. Fusion laser designers have been developing systems to meet these objectives. They have designed 100-300 kJ laser systems for target ignition studies. This activity has produced the Nova harmonically converted glass laser system design at LLNL and the Antares CO 2 laser system design at LANSL. Fusion laser development activities to meet the goals of scientific feasibility are just beginning. Two types of laser systems are being considered. The first design is for a low cost, short wavelength, 3-5 MJ laser to quantify target gain responses for all ICF applications. The second design is for an efficient (~> 10%), high repetition rate ( ~ 5 Hz) laser to serve as a reactor driver. We feel that both of these goals are attainable with continued effort and inspiration. 1.2. Outline

In the remainder of this review article, we present an overview of laser technology that is the present basis for fusion laser design. (2~ The technology elements have been verified by the successful

High Power Pulsed Lasers

7

Fig. 1. The twenty-beamShivaLaser Systemprovides more than 20 TW on a laser fusiontargetin a 100 ps pulse.

operation of many Nd :glass fusion laser systems, CO 2 laser systems, and atomic iodine systems. They are also being used for KrF system design studies. We have organized the remainder of this paper into four sections. In Section 2, we develop the paraxial ray equation from Maxwell's equations. By ificluding linear and nonlinear terms, this equation describes the propagation of laser light from the laser oscillator, through the amplifiers, telescopes, isolators, and the focus lens to the target. In Section 3, we

describe laser gain media and provide examples of the four most important fusion laser systems: Nd:glass, CO2, atomic iodine, and KrF. HF, which was studied as an example of a low cost chemical laser, (21a'b~ is not presented here because of space considerations. Next we discuss the physics of light propagation through actual laser components. Finally, we outline generally used philosophies and methods for the organization of laser components into a working system.

8

Holzrichter et al.

successful because if the beam is so badly distorted that perturbation analysis is not applicable, the beam is unusable for experimentation. The derivation of the paraxial wave equation from Maxwell's equations in optically active media has been given by Lax et al. (21) Here we shall outline how the paraxial approximation is obtained and describe the circumstances which make it valid for use in laser design. Consider a dielectric medium which is source-free (no charge or currents), and complex laser light electric field E and magnetic field H oscillating with angular frequency o~ (typically 6 X l 0 TM r/s). Then Maxwell's equations are as follows (inks units):

Target Gain vs Laser Energy

I

I

I

I

100

10 c~

t~

-~ 10-1

i0-2

10-3 1044

I 0.01

J

I

I

0.1

1.0

10

100

curl E = - io~/~oH

(1)

curlH = i~0( e o E + P )

(2)

Energy in MJ

Fig. 2. The shape of the gain vs laser energy curve shows a supralinear increase in gain vs laser energy near 100-200 kJ. This is the ignition condition, where the fuel burn products cause a significant temperature increase. At higher input energies, the gain saturates due to fuel burnup and additional energy of compression. The rectangles indicate performance uncertainties of targets and systems which are now being analyzed.

(3)

div(H) = 0

(4)

In these equations, P is the complex dipole moment density (polarization) at frequency ~0, which in general is nonlinear in E. From these equations, it follows that

2. PARAXIAL WAVE OPTICS In a large laser system, the total path length along which the laser beam travels may be several hundred meters. In propagating this distance, diffraction causes the light wave to undergo substantial changes in its spatial structure. The spatial structure of the beam is important because it affects both the energy the laser can deliver without damaging optical components and the smallness of the spot formed as the beam is focused onto the target. In Section 4, we shall discuss in more detail the propagation of laser beams in large fusion lasers. In this section, we shall review the mathematical techniques used to analyze diffraction and introduce some of the physical phenomena which are important in laser beam propagation. Almost all of the important aspects of laser beam propagation may be discussed in terms of the paraxial approximation to Maxwell's equations. In the paraxial approximation, the fields are expressed in terms of deviations from a uniform monochromatic plane or spherical wave. The equations for the deviations are considerably easier to solve than Maxwell's equations themselves. This approach is

div(r + e / % ) = 0

(V 2 + k2)E = grad d i v E -

k2P/%

(5)

where k = ~o/c. The paraxial approximation is obtained by writing E = A # kz, where A is the field envelope in space and time. By expanding the Helmholtz operator in Eq. (5) we obtain (V 2 +

kZ)E=eikZ(V2 +2ikO/~z +

O2/3zZ)A (6)

where V~ = 02/0x2 +

O2/Oy2

(7)

We then make three assumptions about the beam which allow us to simplify Eq. (6):

2ikOA/Oz >>0 2 A / ~ z 2

(8a)

grad divE ~ 0

(8b)

= 0

(8c)

Equation (8a) is the condition that the envelope be slowly varying over a distance of several wavelengths, and Eq. (8b) and (8c) state that the field must be

High Power Pulsed Lasers

9

approximately transverse to the direction of propagation (the propagation axis) and change slowly in the direction perpendicular to the propagation axis. The consistency of these assumptions is the subject of ref. 21. The paraxial wave equation results from inserting the approximation in Eq. (8) into Eq. (6) to yield

(2ikO/Oz +

V~ )A = k 2 p / %

(9)

Note that if the medium is isotropic, P is parallel to E (and A). Anisotropy is a complication which we shall not elaborate on here. The validity of the paraxial approximation depends on the smallness of a parameter f, defined as the ratio of the wavelength of the light ( ~ 10 -4 cm) to a typical transverse beam structure dimension w0 ( ~ 10 - 2 c m )

f = )t/2~rw0

(10)

In the case where P = 0 (free space), the corrections to Eq. (6) are of order f 2 . For media with gain or nonlinear response to the light (P ~ 0), there are also corrections of order gX, where g is a growth or gain coefficient with units of inverse length, and ?t is the wavelength. Thus, as long as any nonlinear process does not change the wave significantly in a distance of a few wavelengths, the paraxial equation remains valid. Typically, in situations which have arisen to date, f2 is of order 10 -5, and the product gYt is of the order of 10 -4. Thus, the paraxial approximation is an accurate laser analysis tool. An attractive feature of the paraxial wave equation is that it lends itself naturally to solution by Fourier analysis in the transverse spatial plane. Thus, at any given plane z = z0, we write the field A as a Fourier integral:

A(r, z) =f

E

[

--'q--

2a

Ii

Unit plane wave

I

-0.02

0 -.

0.02

0.04

x (microns)

Fig. 3. The clipping of a uniform plane wave by a hard edged aperture. The wavelength of the light is 1 /~m, and the size of the aperture (2a) is 200/Lm.

As an example of this procedure, consider a simple one-dimensional problem: the clipping of a laser beam by a hard-edged aperture. This is shown in Fig. 3. The laser beam emerging from the aperture is constant in amplitude and phase and drops to zero outside the aperture. The Fourier spectrum of the beam is

+(K,o):faadxei'X=

2a ( sin@-~a)

(13)

where 2a is the aperture width. From Eq. (12), the Fourier transform at plane z is

~( K' z ) = 2a( Sin =-----~a ) exp- iKzz

(14)

which may be inverted to find E(x, z). This has been calculated for a laser beam of wavelength 1 /~m, impinging on an aperture of 200/~m width. Figures (4) and (5) show the field amplitude after propagating 1 cm and 50 cm, respectively. 1.4

(11)

1.2

In free space, P = 0, and substituting Eq. (11) into Eq. (9), we find the solution of Eq. (9) to be ~b(g, z) = ~(~, z0)exp -

iKa(z - Zo)/2k

== 1.o ~' 0.8

{

>. 0.6

(12) =

Free space propagation is therefore carried out easily by inserting Eq. (12) in Eq. (11). The formalism is readily handled with numerical methods on computers, where fast Fourier transforms are used to compute rapidly the propagation of the laser pulse down the laser chain.

0,4

0.2 I -0.04

--0.02

0

0.02

0.04

x (microns)

Fig. 4. The electric field in the near field of the aperture of Fig. 3. The beam has propagated only 1 era.

10

Hoizrichter et al.

0.12

--

I

I

q

I

I

I

I

I

envelope of the wave at that frequency A~= A(0~):

_~ |

~=E 0.10

-- Xo(,O,)+ x,(,Ol)A

0.08

+X2(iOl)A 2+X3(~01)A~+''" o oB

= ~]Xr(~,)(Al) r

~= 0.04

(18)

r

-- 0.02 o

t_

~_. ~ - J ~

-1.0-0.8-0.6-0.4-0.2

0 0.2 x (centimeters)

0.4

0.6 0.8

1.0

Fig. 5. The electric field amplitude in the far field of the aperture of Fig. 3. The beam has now propagated 50 cm.

In this example, it is clear from Eq. (14) that propagation merely changes the phase of the Fourier components. The most important Fourier beam components have x 2, the gain/3 becomes complex, and the ripples predominantly experience phase changes as a result of the nonlinearity. The peak gain e s occurs for x = K0. This component may be viewed as a plane wave travelling at an angle xo/k relative to the background beam, namely,

Opk=

where the B integral is

,= -fdzvI

Fig. 28. The Bespolov-Talonov gain spectra G(x). The horizontal axis is K / t o , where ~0 is the spatial frequency of the maximally growing ripple. At r = to, the tipple gain is e ~.

(63)

This is plotted in Fig. 28. The importance of B is that it measures the maximum gain a ripple of arbitrary spatial frequency may experience. It is therefore a very useful parameter in laser chain design. Minimizing B has been a crucial element in short pulse laser design. This can be accomplished by choosing materials with low nonlinear indices, by reducing the path length of nonlinear material, or by reducing the in-

(271)1/2

(64)

In real systems, an important source of spatial noise (ripples) is the collection of small scattering sites located primarily on the surfaces of the optical components. The spatial frequencies generated by a small obscuration of radius a are of the order of 1/a. Thus, the obscurations of size a ~ 1/~r 0 are the most important sources of spatial modulation. These obscurations derive from dust particles and the erosion of the surfaces of optical components by the flashlamp emission in glass lasers or by the laser beam itself. The number of obscurations increases with the number of amplifier firings. Typically, the size distribution of the obscurations is C(a) = A/~ ~

(65)

High Power Pulsed Lasers

31

where C is the number of scattering sites per unit area whose radius is larger than a, and A ranges from 10 - 6 for very clean components to about 25• 10 - 6 for heavily obscured components. From this formula, the source terms +(~,0) can be determined, and consequently, the maximum allowable value of B (Eq. 61). Another important source of spatial noise is hard edge diffraction. The laser beam may be improperly centered and hit the edge of a lens or amplifier. A hard edge produces a noise spectrum ~(~) proportional to 1/x. This source can be reduced by "apodising" or smoothing the edge so that the dangerous frequencies close to K0 are not present. In addition, automatic beam pointing and centering systems are used to prevent the beam from accidentally hitting apertures.

4.4. Imaging and Relaying: The Spatial Filter We saw above that the nonlinear index of the optical medium causes the diffraction ripples of characteristic spatial frequencies to grow (recall Fig. 6). Damage will occur if these ripples grow too large. One way to prevent their growth is to remove them in a spatial filter.(71)A spatial filter telescope is a combination of two convex lenses separated by the sum of their focal lengths (see Fig. 29). At their common focus, a pinhole of radius R is placed. Thus, only light within R of the axis at the pinhole passes through the filter. We also saw above that the field in the focal plane Of a lens is proportional to the Fourier spectrum of the field impinging on the lens. Thus, the filter passes only transverse spatial frequencies less than the pinhole size. Namely, the filter edge is at rsf, where

kR

Ks/=-- f -

(66)

To be effective in removing the nonlinear ripple

o,l, ou, aL

Pinh~7

/..-'A

Outputbeam1

a

growth, the pinhole clearly must have

Xsf 10, where B is the driver efficiency and G the ICF target gain. For reactor drivers, this is the approximate condition for net energy production and thus ICF power plants.

ACKNOWLEDGMENTS The work described in this paper has been performed by our colleagues throughout the laser community. We thank, in particular, J. L. Emmett, W. F. Krupke, R. O. Godwin, and our associates in the Shiva, Nova, and laser R&D groups at L L N L for their assistance. We also thank C. A. Fenstermacher and his associates at LANL, J. M. McMahon and his associates at NRL, Jay Eastman and his associates at the University of Rochester, J. Gerardo and his associates at Sandia, and our colleagues at KMS Fusion for their contributions to the development of laser

High Power Pulsed Lasers

43

Plasmashutter-~ _ ~ Spatialfilter-~ ~ j ~ l ~ . r Diskamplifiers~

~

"~'.'~' Target ~~J-

Oscillator

Diskamplifiers-7 ~ ~ ~- Faraday Faraday / f 7 ~ rot;~'or i:otator / J ~ Di~kais~176

Fig. 44. The Nova laser chain layout.

technology. This work was performed under the auspices of the U. S. Department of Energy by the Lawrence Livermore National Laboratory under Contract W-7405-ENG-48.

1t. 12.

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