In indirect laser driven inertial confinement fusion (ICF), laser–plasma interaction between the laser and the hohlraum wall produces X-rays, and the X-rays drive the pellet to implosion[
High Power Laser Science and Engineering, Volume. 1, Issue 2, 02000088(2013)
Spatio-temporal evolution of the optical field on a hohlraum wall at the rising edge of a flat-topped pulse
Considering the time delay in different hohlraum wall positions caused by oblique incidence, the spatio-temporal optical field distribution characteristics of a hohlraum wall, especially during the rising edge of a flat-topped pulse, is simulated by a fast Fourier transform method together with chromatography. Results demonstrate that beam propagation along the hohlraum wall is a push-broom process with complex dynamic spatial–temporal evolution. In the first few picoseconds, the optical intensity of the front position increases rapidly, while that of the rear position is relatively weak. The ratio of the optical intensity during the rising edge is smaller than that of the steady state. gradually increases and finally tends to the value of the steady state with time. Calculation also shows that, with shorter total width of the rising edge, of the optical field decreases and the difference compared to the steady state becomes larger. The evolution is more severe with smaller angle of inclination.
1. Introduction
In indirect laser driven inertial confinement fusion (ICF), laser–plasma interaction between the laser and the hohlraum wall produces X-rays, and the X-rays drive the pellet to implosion[
2. Model and theory
According to the national ignition facility’s target chamber structure model, the parameters of the final target chamber structure are as follows: laser wavelength , beam size , 10-order super-Gaussian beam with waist radius . After passing through a lens with focal length , the laser beam passes through the orifice with diameter into a cylindrical target chamber with diameter , as shown in Figure
Based on the model shown in Figure
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3. Simulation and analysis
Based on the above model and computing method, first the optical field in the steady state is analyzed. The three-dimensional intensity distribution on the cylindrical surface is shown in Figure
The optical field distribution both at and extracted from the projection is shown in Figure
When considering the temporal characteristics of the laser pulse, 50-order super-Gaussian pulses with pulse width of 1 ns and a rising edge of approximately 50 ps are taken as examples. The optical field distribution changes with time on the hohlraum wall are simulated, as shown in Figure
Combining the optical field changes over time in both the and directions, we can see that the optical distribution on the hohlraum wall is a complex spatio-temporal evolutional process. In Figures
Because of the particularity of spatial and temporal changes in the -direction of the optical field, the optical field along the -direction is carefully analyzed in the following. Parameter represents the pulse sequence in a pulse when it reaches position in the hohlraum wall. Compare the optical field in the steady state and unsteady state with different on the rising edge in Figure
When is small, the intensity difference between and is greater and the optical field distribution is more tilted. When is large, the optical field distribution is more flat. For the steady state, equals 0.849. Figure
When different pulse sequences reach the hohlraum wall, the instantaneous optical field distribution changes a lot. Compared to the steady-state distribution, the optical intensity in the front position is larger than in the rear position and gradually becomes larger at the rising edge. But in the flat-top region of the pulse, the optical field distribution is the same as that in he steady state, and the distribution does not change over time. As temporal characteristics of the rising pulse affect the optical field distribution a lot, the effect of steepness of the rising edge on the optical field changes over time is studied in the following research. We regard the rising edge model as a simple linear model,
Incidentally, the incident light has different angles ( of inclination with respect to the central axis of the hohlraum, the inner ring of 23.5°and 30°, and the outer ring of 44.5°and 50°. For the above-mentioned discussion, the optical field on the inner ring of 23.5° is analyzed as an example. Actually, the optical field on the inner and outer rings and its evolution at the rising edge are different. For different inclination angles, the laser strikes different locations on the hohlraum wall with various power densities and time delays; thus their temporal and spatial distributions are disparate. Specifically, when is smaller (for inner ring), the average power density on the hohlraum wall is smaller, as shown in Figure
4. Conclusion
To conclude, based on the time delay of an oblique incident laser reaching different positions on the hohlraum wall, the optical field evolution over time on the hohlraum wall at a rising edge of a pulse is analyzed by FFT and a chromatographic principle. Results show that the spatial distribution at the rising edge is more tilted than the steady-state distribution. The optical field distribution changes rapidly over time at a rising edge of picosecond order and ultimately tends to the steady state. When the rising edge is steeper, the optical field varies more quickly with time, and the distribution on the rising edge tilts more seriously with a bigger difference from the steady state. The effect of different angles of inclination is also analyzed, showing that the effect is more obvious with smaller angle. The method used for the rising pulse is also applicable to the falling edge of the pulse, which is not explained here due to limited space. Research on the spatial and temporal evolutional characteristics of the optical field on the hohlraum wall provide a finer spatial and temporal intensity model for the research of laser–plasma interaction, which is helpful to the understanding and analysis of relevant physical problems. The shorter the time scale, the more severe the temporal and spatial variation of the optical field at the rising edge, which also provides appropriate reference for shorter time scale physics research.
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Zhaoyang Jiao, Yanli Zhang, Junyong Zhang, Jianqiang Zhu. Spatio-temporal evolution of the optical field on a hohlraum wall at the rising edge of a flat-topped pulse[J]. High Power Laser Science and Engineering, 2013, 1(2): 02000088
Received: Apr. 20, 2013
Accepted: Jun. 17, 2013
Published Online: Nov. 19, 2018
The Author Email: Zhaoyang Jiao (zhyjiao1988@gmail.com)