ppg_plasma.py

Created on January 10, 2023
1.38 KB
#      ** Plasma **  

# * Eq de Maxwell *

# Pc = 0
# μ = μ0
# ε = ε0
# γ ≠ 0

#    ->
# divE = 0
#    ->
# divB = 0
#            ->
# -> ->     ∂B
# rotE = - ----
#           ∂t
#                       ->
# -> ->      ~ ->      ∂E
# rotB = μ0 (γ E + ε0 ----)
#                      ∂t

#////////////////////////////

# * Eq de propagation *

#                       ->
#  ->  -> ->     ->    ∂B
# rot(rot(E)) = rot(- ----)
#                      dt
#
#   ->     ->   ->     ∂  -> ->
# grad(div(E))-ΔE = - --(rot(B)
#                 ->  ∂t
#              ->          ->
#  ->      ~  ∂E       ∂^2 B
# ΔE = μ0 (γ ---- + ε0 ------)
#             ∂t        ∂t^2

#//(champ magnétique E -> B)

#/////////////////////////////
#              ->      
# E0 e^i(Kz-wt)ux

# ΔE = -k^2 Ex

#    | dEx
#    | --- = -i w Ex
#  ->| dt
# dE |
# ---| 0
# dt |
#    |
#    | 0

#       | d^2 Ex
#       | ------ = -w^2 Ex
#     ->|  dt
# d^2 E |
# ----- | 0
#  dt   |
#       |
#       | 0

# Sur X

#                        w^2
# k^2 Ex = i w μ0 γ Ex + ---Ex
#                        c^2

#       w^2
# k^2 = --- + i w μ0 γ
#       c^2
#

#                 w^2 p
# γplasma = i ε0 ------
#                  w

#       w^2             ε wp^2
# k^2 = --- + i w μ0 i -------
#       c^2               w
#               *         *
#// barrer les w avec les "*"

#       w^2 - wp^2
# k^2 = ----------
#          c^2