position and momentum of the particles are given at each position. In solving (A3.2)
and (A3.3), the E and B at each point of particle are interpolated with the values of
the grid points nearby, while (A3.4) and (A3.5) are solved by summing up the
nearby particle contribution near each grid. At each time step, the flow of calculation
is given as shown in Fig. A.2b.
To describe how to model the giant particles in PIC code is out of the present
scope, and the detail numerical methods are explained, i.e., in books [2]. It is noted
that the PIC scheme describes fundamentally collisionless plasma phenomena.
Surprising Progress of Computing
One of the pioneering research with PIC code for laser plasma is carried out to study
resonant absorption [3] as discussed in Chap. 3. The computational research of laserplasma interaction with PIC code started to publish synchronized with ICF research
paper by Nuckolls et al. [7, Chap. 1] in 1972. The PIC simulation has been done with
the code developed to study electron Weibel instability in two-dimensional system.
Due to the restriction of computer speed as shown in Fig. 1.14, the space grid in x
and y was 50 Â 50, and 10
5 giant particles were used for the calculation over 2000
times Δt [4]. Even under such restriction of computer speed, the physics are well
obtained and compared to the corresponding theoretical results.
With the help of progress of computer capability, grand challenge of computing
has also been done for plasma PIC simulation. It is reported that VPIC, a firstprinciples 3D electromagnetic charge-conserving relativistic kinetic particle-in-cell
code, was used for Peta (10
15 ) flops computing at LANL to study laser-plasma
interaction physics [5]. Note that the used numbers are 325 billion particles on
8256 Â 512 Â 512 mesh, namely, about 0.4 trillion particles and 2 billion cells,
200 particles per cell.
With such a progress of computer speed, PIC code is widely used as tool to
compare experimental results, especially in the case of ultra-short pulse relativistic
laser-plasma interaction. Since the pulse duration is very short less than 1 ps, the fulltime simulation is now possible with PIC code even in two or three dimensions.
Contemporary PIC code algorithm for laser plasma with relativistic and ultra-short
pulse is reviewed, for example, in [6, 7]. Reference [6] mainly focuses on the
plasma-based particle acceleration, while [7] focuses on the extension to quantum
electrodynamics (QED) in relativistic laser-plasma interaction. The Coulomb
collision is also important in laser-plasma interaction in cold-dense plasma such as
solid density. Recently, most of PIC code includes the collision term based on
Coulomb binary collision [7]. Field ionization effect is also installed to PIC code
as described in [7]. Now researchers try to include the atomic process such as
ionization and recombination process in PIC code [8]. In addition, ultra-intense
laser and electron interaction are very sensitive to field profile running near the
speed of light, since the electrons highly accelerated by the field are also running
near the speed of light. The interaction time in the same phase among waves and
Appendices
381
and (A3.3), the E and B at each point of particle are interpolated with the values of
the grid points nearby, while (A3.4) and (A3.5) are solved by summing up the
nearby particle contribution near each grid. At each time step, the flow of calculation
is given as shown in Fig. A.2b.
To describe how to model the giant particles in PIC code is out of the present
scope, and the detail numerical methods are explained, i.e., in books [2]. It is noted
that the PIC scheme describes fundamentally collisionless plasma phenomena.
Surprising Progress of Computing
One of the pioneering research with PIC code for laser plasma is carried out to study
resonant absorption [3] as discussed in Chap. 3. The computational research of laserplasma interaction with PIC code started to publish synchronized with ICF research
paper by Nuckolls et al. [7, Chap. 1] in 1972. The PIC simulation has been done with
the code developed to study electron Weibel instability in two-dimensional system.
Due to the restriction of computer speed as shown in Fig. 1.14, the space grid in x
and y was 50 Â 50, and 10
5 giant particles were used for the calculation over 2000
times Δt [4]. Even under such restriction of computer speed, the physics are well
obtained and compared to the corresponding theoretical results.
With the help of progress of computer capability, grand challenge of computing
has also been done for plasma PIC simulation. It is reported that VPIC, a firstprinciples 3D electromagnetic charge-conserving relativistic kinetic particle-in-cell
code, was used for Peta (10
15 ) flops computing at LANL to study laser-plasma
interaction physics [5]. Note that the used numbers are 325 billion particles on
8256 Â 512 Â 512 mesh, namely, about 0.4 trillion particles and 2 billion cells,
200 particles per cell.
With such a progress of computer speed, PIC code is widely used as tool to
compare experimental results, especially in the case of ultra-short pulse relativistic
laser-plasma interaction. Since the pulse duration is very short less than 1 ps, the fulltime simulation is now possible with PIC code even in two or three dimensions.
Contemporary PIC code algorithm for laser plasma with relativistic and ultra-short
pulse is reviewed, for example, in [6, 7]. Reference [6] mainly focuses on the
plasma-based particle acceleration, while [7] focuses on the extension to quantum
electrodynamics (QED) in relativistic laser-plasma interaction. The Coulomb
collision is also important in laser-plasma interaction in cold-dense plasma such as
solid density. Recently, most of PIC code includes the collision term based on
Coulomb binary collision [7]. Field ionization effect is also installed to PIC code
as described in [7]. Now researchers try to include the atomic process such as
ionization and recombination process in PIC code [8]. In addition, ultra-intense
laser and electron interaction are very sensitive to field profile running near the
speed of light, since the electrons highly accelerated by the field are also running
near the speed of light. The interaction time in the same phase among waves and
Appendices
381