Theoretical study of topics in the interaction of lasers and undersized plasmas: THz radiation with counterpulses, Raman plasma diagnostics. 43 4.4 Maximum RBS intensity and theoretical growth rate depending on the external magnetic field.
List of Table
Introduction
- Bubble formation of the laser wake field
- Raman scattering
- Ponderomotive force
When the relativistic gamma factor of the bubble is lower than R/√2, the electrons catch up with the velocity of the bubble (𝑣0). 10 Assuming a wave electric field of the form. the resultant ponderomotive force of one electron is [7]. where a is the normalized vector potential.
Particle In Cell (PIC) simulation
New field solver (Field split method)
Although there are various numerical methods to solve Maxwell's equation, Yee solver has been thought of as one of the standard methods due to the simplicity of the applications and the efficiency of low memory cost [10]. The original Yee solver has a problem with numerical dispersion of 2D and 3D calculations, which can occur in the direction of coordinate axes such as x, y, and z [11]. All units are dimensionless by normalizing time to 1/𝜔0, lengths to 𝜆0, speed to c, electric field to mc𝜔0/𝑒, magnetic field to m𝜔0/𝑒 and current to e𝑛0𝑐.
As shown in equation (2.2), the calculation is performed in 2 steps for a simulation time step. 2.3) and (2.5) refer to the fact that the field values for an entire mesh are precisely moved to the next grid points in each simulation time step. Although the cell size is large, because the calculation is done by transferring field values, there is no distortion of the laser field.
Also, it does not provide a field reflection at the simulation boundary, so it does not need PML boundary.
Lorentz boosted frame
When you travel significantly long distances, it turns out that Yee solver is backwards. propagation, but the field splitting method has no numerical dispersion. Plasma length or position L or x 𝐿/𝛾 𝑜𝑟 𝑑/𝛾. Table 1.1 The parameter comparison between lab frame and boost frame. 𝛾 is the relativistic gamma factor of the moving frame. Although the process of the amplified frame is the same as the calculation of the laboratory frame, the backward signal field has significant noise, and the reasons are given as follows. when the field reverses, the magnetic field becomes as 𝐵𝑧 = −𝐸𝑦. 2.8), the amplitude of backward fields varying with simulation time.
The last thing to do for the boosted frame is to convert data from the boosted frame to the lab frame. To obtain values for a given laboratory frame time, it needs information about several time steps in the amplified frame. It needs to find in each time step the gain x position corresponding to the target laboratory frame time using Eq.
Especially the field ionization method is important for the 2-color laser scheme [19] for Terahertz generation and ion target acceleration. This model shows the ionization rate for one electron, so using the ionization rate the electrons and ions are generated each simulation time step from given ionization energies.
Terahertz radiation by colliding lasers in magnetized plasmas
- Introduction
- Electromagnetic diffusion and growing near cut-off frequency
- Scaling of the THz amplitude
- Conclusion
3.2 (a) is a snapshot of the diffusing fields at different times, obtained from numerical integration of Eq. The diffusive growing nature of the field can be used as a method to transform the plasma oscillation into an electromagnetic wave in free space. Another important effect of the density gradient is that the field growth given by Eq. 3.18) is maintained for a longer time, ultimately leading to stronger THz emission.
To obtain the solution of Eq. 3.30) we evaluate the temporal evolution of 𝑛�1 driven by the rate of the counter pulses. A significant effect of wave breaking is the suppression of the plasma flow by kinetic tuning [46]. In fact, the positive effect of the density gradient is one of the advantages of the field diffusion mechanism.
From analytical theory, we found that the THz amplitude scales with 𝑃2 of the driving pulse, which is verified by one-dimensional PIC simulations. The other is emission enhancement by a driven diffusion mechanism of the electromagnetic field.
Measuring the magnetic field of a magnetized plasma using Raman scattering
Note that we assumed that the relativistic effect can be neglected and that the ions are stationary on the scattering time scale. On the contrary, the wavenumber of the plasma wave for exact backscattering is roughly twice the wavenumber of the pump. Because the phase velocities of the plasma waves involved in RFS and RBS differ greatly from each other, the spectral dependence of the scattered waves on the magnetic field shows a significantly different behavior.
Such a point can be easily seen by representing the frequency of the plasma wave as a function of the phase velocity from Eq. 4.8) and (4.9), and the above-mentioned resonance conditions, the plasma wave frequency can be represented as a function of the magnetic field, both for RFS and RBS, as shown in Figure. In the simulations, the external magnetic field was perpendicular to the propagation of the pump's laser pulse.
4.2 (a)–(c) shows the right-directed field, left-directed field, and k-spectra of the RFS and RBS signals, respectively. Note that when the plasma dimension and the pump pulse are similar, the inhomogeneity of the plasma can cause a broadening of the bandwidth of the scattered signals.
Electron trapping by a transversely ellipsoidal bubble in the laser wake- field acceleration
Model of the ellipsoidal bubble fields
The electromagnetic field in a bubble has an increasing linear region around the center and a thin enveloping region near the edge of the bubble. Indeed the bubble potential is defined as 𝛷 = 𝐴𝑥− 𝜙 using the gauge of 𝐴𝑥 = −𝜙, where 𝐴𝑥 and 𝜙 are the x-component of a vector potential and a scalar potential, respectively (see Sec. 3). Dividing the range of integration at 𝑟 = 𝑅, the final form of the potential becomes for the region of 𝑟 ≤ 𝑅. is a di-logarithm function and.
By then assuming that the potential is constant around the bubble edge, we can state the potential as follows: Here the multiplication factor of 2 before the sheath thickness d is just to ensure that the distance is far enough from R. We also use separate values for the field slopes in x and y directions, i.e. 𝑘𝑥 and 𝑘𝑦. 5.6) and (5.9), we obtain the relationship between the field slopes and the bubble sizes in x and y directions as follows: 5.10) tells us that the elongation of the ellipsoidal bubble is determined by the ratio of the bubble's field slope in each direction.
Here we notice that the scale factor 𝑘𝑥 or 𝑘𝑦 is obtained as the ratio of the slope of the corresponding electric field component and the maximum value of the field slope. 14)) yields the following potential which in turn corresponds to the elliptical shape of the bubble. 5.12), we have neglected the screening terms that are only important near the bubble edge.
Electron trapping in an ellipsoidal bubble
This point gives us an important insight into trapping, since the transversely elongated ellipsoidal bubble appears quite often in the early stage of bubble formation, which is the regime that the spherical theory does not explain trapping. When the pulse spot size is larger than the plasma wavelength, the transverse field slope is somewhat retarded in growth compared to the longitudinal field slope because the laser pulse edge field makes it difficult for electrons to collect around the bubble. the sides. In this way, the delayed increase in the slope of the transverse field forms a transversely elongated ellipsoidal bubble.
To compare the theoretical trapping condition of Eq. 5.19) with PIC simulations, the gamma factor γ0 of the bubble must be calculated. The trapped particles were initially located at the vertical (transverse) edge of the low-momentum bubble, and then began to be trapped near the rear of the bubble. Then the gamma factor of the back side of the bubble can be calculated with [5]. where x is the last position and 𝑑0 is the initial position of trapped electrons in the trapping process.
From the measured slope in x vs. 5.20) the gamma factor of the back of the bubble can be calculated, which is the gray solid line in figure. The gray solid line is the gamma factor of the back of the bubble, the red solid line is 𝑅𝑦 /√2, and the dotted line is 𝑅𝑥/√2, which is the same as the.
Conclusion
Summary and Future work
The theory was limited to a stationary potential, however, the 3D PIC simulation result states that the bubble is variable. An ellipsoidal potential traps electrons in the initial phase more than a spherical potential, so the large laser spot size can help increase the number of accelerated electrons. When the plasma density is low, it is difficult to make an ellipsoidal bubble because it needs a high laser power for a large spot size.
The high-density portion of the plasma is used to create initial electron seeds, after which these seed electrons are accelerated into the low-density portion of the plasma. Although it is not easy to make an elliptical bubble in a real experiment, it is still curious about the low-density case. The bubble field becomes stronger as the laser passes through the plasmas. However, the degree of enhancement is low at low plasma density and it is interesting to study the rate of field strength of the ellipsoidal bubble.
Various PIC techniques were introduced such as high order interpolation, new field solver, field ionization and boosted frame. Other groups use the boosted framework to predict the final electron energy and charges, and it still matches experimental results well.
Moloney, "Generation of electromagnetic pulses from plasma channels induced by femtosecond light strings," Physical Review Letters, vol. Li, et al., "Terahertz radiation from oscillating electrons in laser-induced wake fields," Physical Review E, vol. Sanuki, “Emission of electromagnetic pulses from laser wake fields via linear mode conversion,” Physical Review Letters, vol.
34;Two-color laser-plasma generation of Terahertz radiation using a frequency-tunable half-harmonic of a femtosecond pulse," Physical Review Letters, vol. Ito, et al., "Experimental observation of radiation from Cherenkov wakes in a magnetized plasma," Physical Review Letters , vol. Sprangle, "Electron injection into plasma wake fields by colliding laser pulses," Physical Review Letters, vol.
Esarey, “Plasma electron capture and acceleration in a plasma wake field using a density transition,” Physical Review Letters, vol. Blumenfeld, et al., "Ionization-induced electron capture in ultrarelativistic plasma awakenings," Physical Review Letters, vol.
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