Diagnostics

TimeHistoryDiagnostics( maxwell_solver, kernel_smoother_0, kernel_smoother_1 )

Context to save and plot diagnostics

• maxwell_solver : Maxwell solver
• kernel_smoother_0 : Mesh coupling operator
• kernel_smoother_1 : Mesh coupling operator
• data : DataFrame containing time history values

Outputs

• KineticEnergy: $\frac{1}{2} \sum \omega_i v_i^2$
• Kineticspi: Zeeman energy

Momentums: compute integrals of f

• Momentum1 : $\sum x_i \omega_i$
• Momentum2 : $\sum x_i \omega_i s1$
• Momentum3 : $\sum x_i \omega_i s2$
• Momentum4 : $\sum x_i \omega_i s3$
• Momentum5 : $\sum \omega_i s1$
• Momentum6 : $\sum \omega_i s2$
• Momentum7 : $\sum \omega_i s3$
• Momentum8 : $A_y \sum div(\rho) \omega_i s2 + A_z div(\rho) \omega_i s3$
• Momentum9 : $- A_y div(\rho) \omega_i s1$
• Momentum10 : $- A_z div(\rho) \omega_i s1$
• PotentialEnergyE1 : $\frac{1}{2} E_x^2$
• PotentialEnergyE2 : $\frac{1}{2} E_y^2$
• PotentialEnergyE3 : $\frac{1}{2} E_z^2$
• PotentialEnergyB2 : $\frac{1}{2} B_y^2$
• PotentialEnergyB3 : $\frac{1}{2} B_z^2$
• Transfer : $\sum (v_i \cdot e_{x,i}) w_i$
• ErrorPoisson : difference between $E_x$ computed with Maxwell Solver et $E_x$ computed from charge

pic_diagnostics_transfer( particle_group, kernel_smoother_0, 
                        kernel_smoother_1, efield_dofs, transfer)

Compute $\sum_{particles} w_p ( v_1,p e_1(x_p) + v_2,p e_2(x_p))$

• particle_group
• kernel_smoother_0 : Kernel smoother (order p+1)
• kernel_smoother_1 : Kernel smoother (order p)
• efield_dofs : coefficients of efield

solvepoisson!( efield, particlegroup, kernelsmoother, maxwellsolver, rho )

Accumulate rho and solve Poisson

• particle_group : Particles
• maxwell_solver : Maxwell solver (FEM 1D)
• kernel_smoother_0 : Particle-Mesh method
• rho : preallocated array for Charge density
• efield_dofs : spline coefficients of electric field (1D)