We present a study of the short-time scale (< 250 ns) fluid dynamic response of water to a fiber-delivered laser pulse of variable energy and spatial profile. The laser pulse was deposited on a stress confinement time scale. The spatial profile was determined by the fiber core radius r (110 and 500 microns) and the water absorption coefficient {mu}{sub 2} (200 and 50 l/cm). Considering 2D cylindrical symmetry, the combination of fiber radius and absorption coefficient parameters can be characterized as near planar (1{mu}{sub 2} greater than r), symmetric (1/{mu}{sub 2}=r), and side-directed (1/{mu}{sub 2} less than r). The spatial profile study shows how the stress wave various as a function of geometry. For example, relatively small absorption coefficients can result in side-propagating shear and tensile fields

Amendt, P.

Celliers, P.

Da Silva, L.

London, R. A.

Maitland, D. J.

Matthews, D.

Strauss, M.

Visuri, S. R.

UNT Digital Library

March 7, 1997This is a preprint of a paper intended for publication in a journal or proceedings.  Sincechanges may be made before publication, this preprint is made available with theunderstanding that it will not be cited or reproduced without the permission of theauthor.UCRL-JC-126834PREPRINTD. J. Maitland, P. Celliers, P. Amendt,L. Da Silva, R. A. London, D. Matthews,M. Strauss, and S. R. VisuriThis paper was prepared for submittal to theSociety of Photo-Optical Instrumentation Engineers BiOS ’97San Jose, CaliforniaFebruary 8-14, 1997Simulations of Laser-Initiated Stress WavesLawrenceLivermoreNationalLaboratoryDISCLAIMERThis document was prepared as an account of work sponsored by an agency ofthe United States Government.  Neither the United States Government nor theUniversity of California nor any of their employees, makes any warranty, expressor implied, or assumes any legal liability or responsibility for the accuracy,completeness, or usefulness of any information, apparatus, product, or processdisclosed, or represents that its use would not infringe privately owned rights.Reference herein to any specific commercial product, process, or service by tradename, trademark, manufacturer, or otherwise, does not necessarily constitute orimply its endorsement, recommendation, or favoring by the United StatesGovernment or the University of California.  The views and opinions of authorsexpressed herein do not necessarily state or reflect those of the United StatesGovernment or the University of California, and shall not be used for advertisingor product endorsement purposes.Simulations of Laser-Initiated Stress WavesDuncan J. Maitland, Peter Celliers,  Peter Amendt, Luiz Da Silva,Richard A. London, Dennis Matthews, Moshe Strauss‡ and Steven R. VisuriLawrence Livermore National Laboratory, Livermore, CA 94550;‡Nuclear Research Center, Negev, P.O. Box 9001, Beer Sheva, IsraelABSTRACTWe present a study of the short-timescale (less than 250 ns) fluid dynamic response of water to a fiber-delivered laserpulse of variable energy and spatial profile.  The laser pulse was deposited on a stress confinement timescale.  Thespatial profile was determined by the fiber core radius, r,  (110 and 500 microns) and the water absorption coefficient,µa, (200 and 50 1/cm).  Considering 2D cylindrical symmetry, the combination of fiber radius and absorptioncoefficient parameters can be characterized as near planar (1/µa greater than r), symmetric (1/µa ≈ r), and side-directed(1/µa less than r).  The spatial profile study shows how the stress wave varies as a function of geometry.  Forexample, relatively small absorption coefficients can result is side-propagating shear and tensile fields.2. INTRODUCTIONThe evolution of stress waves emanating from laser energy deposited at the tip of an optical fiber isexamined in this report.  The  influence of geometry on the stress wave features is demonstrated.  For example,assuming that tension and shear are desirable stress wave features for a given clinical application,  the selection of thefiber radius relative to the deposition depth can be chosen to optimize the tension and shear of the generated stresswave.  The preliminary results provided by these simulations suggest that the compressive, tensile and shearcharacteristics of the stress wave can be engineered by controlling the absorption depth of the laser energy, the fibertip geometry, and, implicitly, the deposited energy.3. MODELING METHODSThe simulations were performed in two stages.  The initial energy distribution at the fiber tip wascalculated with a 2D axi-symmetric (r and z) Monte Carlo photon propagation code1.  The Monte Carlo code wasused to approximate the sharp radial cutoff of energy deposition while maintaining the appropriate exponentialenergy deposition along z.  The calculated energy distribution was then used as an initial condition in thehydrodynamic computations performed by LATIS3D.  Figure 1 shows a typical initial pressure distribution.  Thefiber was hydrodynamically modeled as a perfect reflector with zero normal-velocity fields.  The region around thefiber was modeled as water with a Lawrence Livermore National Laboratory generated equation-of-state (EOS)2.After the fiber-water geometry was initialized, the hydrodynamic package was used to explicitly time-step thepropagation of the stress wave that results from the energy deposition at the tip of the fiber.  Figure 2 shows asnapshot at 150 ns after start of the problem depicted in Figure 1.cylindrical symmetry300 600 9007003500r (microns)z (microns)0 25 50 75 100pressure (bar)Total energy: 1.0 mJµa-1: 20 µmFiber radius: 500 µm  (+ 20 µm cladding)Initial peak p: 97 BarInitial peak ∆T: 25 oC time = 0 ns1/2 optic fiberFigure 1.  An example of the initial conditions used by the LATIS3D program.The cylindrical half-space is shown with the fiber depicted as the black region.The model uses a water equation-of-state in all other regions of the simulation.LATIS3D is a discontinuous finite element code currently capable of implementing hydrodynamic,radiation diffusion and thermal diffusion physics.  LATIS3D is a multi-physics simulation program that is similarto  LATIS, which has previously been described3.  The code names are based on an acronym standing for LAser-TISsue.  The physics processes considered by the two codes are equivalent.  However, LATIS3D is based on adevelopmental code, ICF3D4,5.  The 2D hydrodynamic results presented here used arbitrary Lagrangian-Eulerianhydrodynamics with reflective boundary conditions. The hydrodynamic algorithm is based on the numericalsolution to the mass, energy and momentum conservation equations along with the EOS table.  The solution to theconservation equations results in time and space dependent values of pressure (p), density (ρ) and velocity (u).  TheEOS is used to look up the internal energy (e) and temperature (T) that correspond to p, ρ and u.4. EXPERIMENTAL VALIDATION OF THE SIMULATIONSAs previously described, we used a Mach-Zehnder interferometer arrangement to provide a sensitive andquantitative measurement of the refractive index variations produced through the compression of the liquid withinthe stress transient6.  The use of interferometry to measure the refractive index changes caused by stress fieldtransients is a well known technique7,8.  This analysis involves the generation of a two-dimensional phasedistribution from the interferogram, followed by Abel inversion9 to extract the three-dimensional refractive indexdistribution created by the stress wave.  The final product of these experiments and analysis is a map of the refractiveindex changes (∆n) caused by the space and time dependent stress wave.The experimentally generated ∆n maps can be directly compared with similar maps generated from thesimulation results.  In water, the relationship between refractive index and density, temperature and wavelength iswell known10.  Hence, the simulations were converted into the refractive index maps.300.00 600.00 900.00700.00350.000.00r (microns)z (microns)-40.00 -20.00 0.00 20.00 40.00pressure (bar)Figure 2.  Stress wave at 150 ns.  The pressure and relative velocity fields areshown for the problem described in Figure 1.  Compression and tension are bothobserved.  The velocity gradients perpendicular to the vector directions indicateshear fields.  In soft tissue the shear fields shown would be qualitatively similar,but altered somewhat by the shear strength.5. RESULTSA qualitative comparison of experimental and simulated results is provided by the refractive index mapsshown in Figure 3.  The general characteristics agree well.  The relaxation of the deposited, stress-confined energyproduces a traveling compression wave that, due to the cylindrical symmetry, is followed by a tensile wave.  Twonoticeable differences between the experimental and simulated images are the geometry of the tensile wave and thedeposition region.  The experimental index map does not show that, at 250 ns after the laser was turned on,cavitation bubbles are formed within the deposition region.  The water within the deposition region "failed" due tothe tensile stresses acting on nucleation sites in the water.  Our current belief is that the differences between thesimulated and experimental tensile waves is due to the model's inability to account for the cavitation of the water.This will be remedied in the futyre since we have an ongoing effort to incorporate material strength and failure intoLATIS and, eventually, LATIS3D11.  The differences in the deposition region are, in part, also due to the cavitationbubbles' impact on refractive index (both density and temperature) in the deposition region.  The simulations' soundspeed is a few percent faster than the experiment.  This error is a result of an incorrect compressibility in the EOSand will be corrected in future simulations.The peak tensions in the measured and simulated index maps (Figure 3.) are approximately -150 bar each.Since no cavitation bubbles were noted outside the deposition region in the experiment, such tensile stresses did notcause "failure" in the water.  Further, since the experimental and simulated tensile magnitudes are approximatelyequal (though the profiles are different), the simulation may be used to estimate that the tensile wave was -250 barwhen it was just outside the deposition region.  Thus an experimental wave of 30 ns in duration with a peak tensionof -250 bar did not cause cavitation bubbles.  Paltauf et.al. estimated that tensile waves of -10 bar or more wouldcause cavitation in water12 , based on experiments with, approximately, a 300 ns-long tensile wave.  In order toexplain this difference, we postulate that the strength of water is a dynamic function of the pressure history.Figure 4 presents the simulation results for two different geometric cases.  The differences in the two cases(Figures 4a-4c or 4d-4f) exhibit the geometric influence on tensile and shear stresses.  The geometry of the deliverysystem may be engineered to optimize stresses radially, for example, as in Figures 4d-4f.  Figures 4a-4c are for thesame case used in the Figure 3. index maps.optic fiber240 µmoptic fiber240 µmcompressive wavecompressive wavetensile wavetensile waveFigure 3.  A comparison of experimental and simulated refractive index maps.  The images are at 250ns after the laser was turned on.  The experimental pulse length was 5 ns.  The energy deposited was1.0 mJ into a 200 cm-1 absorption coefficient.  Both results exhibit similar qualitative characteristicsfor the leading compression wave, trailing tensile wave and energy deposition region.  In both figures,the leading compression wave corresponds to approximately +200 bar and the trailing tensile waveapproximately -150 bar.0 200 400 600800600400200r (microns)z (microns)0 500 1000 1500 2000pressure (bar)Total energy: 1.0 mJµa-1: 50 µmFiber radius: 100 µm  (+ 20 µm cladding)Initial peak P: 1700 BarInitial peak ∆T: 77 oC0 ns- 4 0 0- 1 0 02001002 020 200 400 600800600400200r (microns)z (microns)-450 -300 -150 0 150 300 450pressure (bar)100 ns5 00- 1 5 0- 1 0 0- 5 00150 1005 00 200 400 600800600400200r (microns)z (microns)-200 -100 0 100 200pressure (bar)200 ns3001801206 02 51 51 00 200 400 60002004006008001000r (microns)row0 90 180 270 360pressure (bar)Total energy: 1.0 mJµa-1: 200 µmFiber radius: 100 µm  (+ 20 µm cladding)Initial peak P: 356 BarInitial peak ∆T: 33 oC0 ns- 1 0- 1 1 03 01 050 200 400 60002004006008001000r (microns)z (microns)-130 0 130pressure (bar)100 ns1 00- 1 0- 4 0- 3 0- 2 0- 1 001 02 01 0200 400 60002004006008001000r (microns)z (microns)-40 -20 0 20 40pressure (bar)200 nsFigure 4.  Simulated stress wave propagation from fiber tip.  The smaller absorption coefficient,µa, for figures d.-f. causes the peak stresses to be side-directed.  Ignoring all other design factors,the location of the peak stress can be adjusted by the appropriate selection of µa and r, the fiberradius.6. CONCLUSIONWe have shown that LATIS3D can quantitatively predict the stress wave features for a laser-initiated stresswave propagating from an optic fiber.  The refractive index maps also agree well with the experimental results.  Theresults show how the energy delivery geometry, which is defined by the absorption coefficient and the fiber radius,influences the evolution of the stress wave.7. ACKNOWLEDGMENTSThis work was performed under the auspices of the US. Department of Energy by the Lawrence Livermore NationalLaboratory under Contract W-7405-ENG-48.8. REFERENCES1. S.L. Jacques and L. Wang, "Monte Carlo Modeling of Light Transport in Tissues," in Optical-ThermalResponse  of Laser-Irradiated Tissue, (eds. A.J. Welch and M.J.C. van Gemert) pp. 73-100, Plenum Press,(1995).2. D. A. Young and E. M. Corey, J. Appl. Phys. 78, 3748, (1995).3. R. A. London, M. E. Glinsky, G. B. Zimmerman, D. S. Bailey, D. C. Eder and S.L. Jacques, "Laser–TissueInteraction Modeling with LATIS," submitted to Applied Optics, February, 1997.4. A.I. Shestakov, M.K. Prasad, J.L. Milovich, N.A. Gentile, J.F. Painter, G. Furnish and P.F. Dubois, "TheICF3D Code," Inertial Confinement Fusion Quarterly Report, UCRL-LR-124418, in print (1997).5. D.S. Kershaw, M.K. Prasad, M.J. Shaw, and J.L. Milovich, "3D unstructured mesh ALE hydrodynamics withthe upwind discontinuous finite element method," submitted to J. Comp. Phys.6. P. Celliers, L.B. Da Silva, N.J. Heredia, B.M. Mammini, R.A. London and M. Strauss, "Dynamics of laser-induced transients produced by nanosecond duration pulses,"  in Lasers in Surgery:  AdvancedCharacterization, Therapeutics and Systems VI Proc. SPIE Vol. 2671, pp. 22-27, Society of Photo-OpticalInstrumentation Engineers (1996).7. B. Ward and D.C. Emmony, "Interferometric studies of the pressures developed in a liquid during infrared-laser-induced cavitation-bubble oscillation," Infrared Phys., 32, pp. 489-515 (1991).8. M. Kujawinska, "Spatial phase measurement methods," in Interferogram Analysis, (eds. D.W. Robinson andG.T. Reid) pp. 140-193, IOP Publishing Ltd., Bristol (1993).9. W.R. Wing and R.V. Neidigh, "A rapid Abel inversion," Am. J. Phys., 39 pp.760-764 (1971).10. I. Thormahlen, J.Straub , and U. Grigull, "Refractive index of water and its dependence on wavelength,temperature and density," J. Phys. Chem. Ref. Data 14, 933-945 (1985)11. M. Glinsky, R.A. London, and D. Bailey, "LATIS modeling laser-induced midplane and backplanespallation," in Laser-Tissue Interactions VIII Proc. SPIE Vol. 2675, Society of Photo-Optical InstrumentationEngineers (1997).12. G. Paltauf, E. Reichel and H. Schmidt-Kloiber, "Study of different ablation models by use of high-speed-sampling photography," in Laser-Tissue Interactions III Proc. SPIE Vol. 2675, pp. 343-352, Society of Photo-Optical Instrumentation Engineers (1992).Technical Information Department  • Lawrence Livermore National LaboratoryUniversity of California • Livermore, California  94551

Simulations of laser-initiated stress waves

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Simulations of laser-initiated stress waves

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