Commit 4c77a6c9 authored by Mathieu RASSON's avatar Mathieu RASSON

Instability figures

parent fb4967be
......@@ -60,8 +60,11 @@
"import numpy as np\n",
"from FCN import CrankNicolsonFilamentation\n",
"\n",
"# Beam\n",
"# Physics\n",
"c = 3e8\n",
"mu = 4*np.pi*1e-7\n",
"\n",
"# Beam\n",
"lambd = 0.7e-6\n",
"w0 = 1e-3\n",
"tp = 85e-15\n",
......@@ -115,8 +118,8 @@
"metadata": {},
"outputs": [],
"source": [
"delta_z = 2e-4\n",
"z_max = 4\n",
"delta_z = 3e-3\n",
"z_max = 2.7\n",
"n_z = int(z_max/delta_z)\n",
"\n",
"crank = CrankNicolsonFilamentation()\n",
......@@ -193,16 +196,22 @@
"metadata": {},
"outputs": [],
"source": [
"listemax = 1/(c*mu) * np.array([np.amax(np.abs(E[i,:,:])**2) for i in range(crank.n_z)])\n",
"#listemax = np.array([np.amax(np.abs(E[i,:,:])**2) for i in range(crank.n_z)])\n",
"listemax = np.array([np.amax(np.abs(E[i,2,:])**2) for i in range(crank.n_z)])\n",
"#listemax = 1/(c*mu) * np.array([np.amax(np.abs(E[i,2,:])**2) for i in range(crank.n_z)])\n",
"\n",
"maxi = crank.n_z\n",
"maxi = 736\n",
"print(crank.n_z)\n",
"print(1/(c*mu))\n",
"\n",
"plt.figure()\n",
"plt.plot(np.real(crank.z_pts[:maxi]), listemax[:maxi]/Pcr)\n",
"plt.plot(np.real(crank.z_pts[:maxi]), listemax[:maxi])\n",
"plt.ylim(0, 1.5e15)\n",
"plt.xlim(2, 2.3)\n",
"plt.xlabel('Propagation distance (m)')\n",
"plt.ylabel('Squared field amplitude ($V^2 \\cdot m^{-2}$)')\n",
"plt.savefig('filamentation_2P.png', dpi=300)\n",
"plt.ylabel('Intensity ($W \\cdot m^{-2}$)')\n",
"#plt.ylabel('Squared Field Amplitude ($C^2 \\cdot m^{-2}$)')\n",
"#plt.savefig('field_kerr_instability.png', dpi=300)\n",
"plt.show()"
]
},
......@@ -220,7 +229,24 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"The two caracteristic distances are around 5 mm. Therefore $\\Delta z$ has to be chosen around 0.5 mm and 0.1 mm is even better."
"The two caracteristic distances are around 5 mm. Therefore $\\Delta z$ has to be chosen around 0.5 mm and 0.1 mm is even better.\n",
"\n",
"Convergence achieved:\n",
"* $P = 2 P_{cr}$\n",
"* Saturation at $E^2 = 3 \\cdot 10^{17} \\, C^2 \\cdot m^{-2}$ and $\\rho = 5 \\cdot 10^{22} \\, m^{-3}$\n",
"* $z_{max} = 4 \\, m$ (article)\n",
"* $r_{max} = 2 \\, mm$\n",
"* $t_{max} = \\pm 2 \\cdot 10^{-13} \\, s$\n",
"* $\\Delta z = 0.1 \\, mm$\n",
"* $n_t = n_r = 150$\n",
"\n",
"Stability issues:\n",
"* $P = 2 P_{cr}$\n",
"* $z_{max} = 2.7 \\, m$ (just after Kerr collapse)\n",
"* $r_{max} = 2 \\, mm$\n",
"* $t_{max} = \\pm 2 \\cdot 10^{-13} \\, s$\n",
"* $\\Delta z = 3 \\, mm$\n",
"* $n_t = n_r = 150$"
]
},
{
......@@ -231,10 +257,15 @@
"source": [
"listemax = np.array([np.amax(rho[i,:,:]) for i in range(crank.n_z)])\n",
"\n",
"maxi = crank.n_z\n",
"maxi = 736\n",
"\n",
"plt.figure()\n",
"plt.plot(np.real(crank.z_pts[:maxi]), listemax[:maxi])\n",
"plt.ylim(0, 6e22)\n",
"plt.xlim(2.0, 2.3)\n",
"plt.xlabel('Propagation distance (m)')\n",
"plt.ylabel('Charge density ($m^{-3}$)')\n",
"#plt.savefig('charge_kerr_instability.png', dpi=300)\n",
"plt.show()"
]
},
......
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