{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Microwave grouper" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "source": [ "The processes of beam bunching in a microwave buncher can be analyzed using the equations of longitudinal dynamics:\n", "\n", "Equation for the change in particle momentum\n", "$$\n", "\\frac{dp_z}{dt} = eE(z)\\cos(\\omega t + \\phi_0)\n", "$$\n", "\n", "where $p_z$ is the longitudinal momentum of the particle, $e$ is the charge of the electron, $E(z)$ is the distribution of the magnitude of the longitudinal electric field along the axis of the buncher, $\\omega$ is the angular frequency, and $\\phi_0$ is the initial phase. Taking into account that the longitudinal momentum of a particle is $\\beta\\gamma m$, where $m$ is the rest mass of an electron, and $\\beta$ and $\\gamma$ are the usual relativistic factors of particles, equation can be rewritten as\n", "\n", "Equation for the change in longitudinal phase space\n", "\n", "$$\n", "\\frac{d(\\gamma\\beta)}{dt} = \\left(\\frac{e}{mc}\\right)E(z)\\cos(\\omega t + \\phi_0)\n", "$$\n", "\n", "The derivative $\\frac{d\\gamma \\beta}{dt} = \\dot{\\gamma}\\beta + \\dot{\\beta}\\gamma $, where the dot indicates a derivative with respect to time, can be transformed as follows:\n", "$$\n", "\\dot{\\gamma} = \\frac{d}{dt} \\frac{1}{\\sqrt{1-\\beta^2}} = \\beta \\gamma^3 \\dot{\\beta}.\n", "$$\n", "\n", "Then takes the form:\n", "$$\n", "\\frac{d\\gamma \\beta}{dt} = \\gamma \\dot{\\beta} (\\gamma^2 \\beta^2 + 1) = \\frac{e}{mc} E(z) \\cos(\\omega t + \\varphi_0).\n", "$$\n", "\n", "If we assume that the longitudinal velocity of the particle is much smaller than the transverse velocity $\\gamma \\beta_{\\alpha, r} \\ll \\gamma \\beta$, then $\\gamma^2 = \\gamma^2 \\beta^2 + 1$, and transitioning to the longitudinal coordinate $dt = \\frac{dz}{\\beta c}$, we get:\n", "$$\n", "\\frac{d\\beta}{dz} \\frac{\\beta }{(1-\\beta^2)^{3/2}} = \\frac{E(z)}{U_0} \\cos(\\varphi + \\varphi_0),\n", "$$\n", "\n", "where $U_0 = mc^2/e$ - is the rest energy of the electron in volts, $\\varphi$ - is the phase of the moving particle relative to the electrical component of the CBM field:\n", "$$\n", "\\frac{d\\varphi}{dz} = \\frac{\\omega}{\\beta c}.\n", "$$" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "ExecuteTime": { "start_time": "2024-04-02T06:03:40.158544Z" }, "collapsed": false, "is_executing": true, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "D:\\TMP\\ipykernel_8688\\75803242.py:22: RuntimeWarning: invalid value encountered in power\n", " dbeta_dz = (E / U0) * np.cos(phi + phi_0) * ((1 - beta**2)**(3/2)) / beta\n" ] }, { "data": { "image/png": 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+DKU4Ax8AwCKEUgAAAGVMzZo19dhjj2n16tX6+eefdfHFF+vyyy/Xn3/+aXVpyM+XoVTewc4BALBAhNUFAAAAwL/69OnjcvuRRx7RzJkz9eOPP+qss86yqCoUYBi+G1NK4vA9AIDlCKUAAADKsJycHL3//vs6duyY2rZta3U5yOvAAenQIcf1Bg28v3wzlNq0ScrJcZyNDwAAPyKUAgAAKIN+//13tW3bVidOnFB8fLw+/PBDNW3atNB5s7KylJWV5bydkZEhSbLb7bLb7V6vzVymL5YdTGzr1ilCklGzprIjIyVvb49q1RQRFSXbyZOy//OPVLeu2w+ljYID7RQcaKfARxt5zt1tRSgFAABQBjVu3Fhr1qzR4cOHNX/+fA0dOlRLly4tNJiaMmWKJk+eXGD64sWLVa5cOZ/VmJqa6rNlB4OaS5aotaR9FSvqh88/98k6Lq5SRQn//qtVc+dqb8uWHj++rLdRsKCdggPtFPhoI/dlZma6NR+hFAAAQBkUFRWlhv+NU9S6dWutWrVKzz77rF588cUC806cOFHjx4933s7IyFCtWrXUvXt3JSYmer02u92u1NRUdevWTZGRkV5ffrAIW7VKkpR0/vnq1auXT9YR3ry59O+/Or9KFRkerIM2Cg60U3CgnQIfbeQ5s1f16RBKAQAAQLm5uS6H6OUVHR2t6OjoAtMjIyN9unPu6+UHvC1bJElhjRsrzFfb4b+xqiK2b5dKsI4y30ZBgnYKDrRT4KON3OfudiKUAgAAKGMmTpyonj17qnbt2jpy5Ijmzp2rb7/9Vl9++aXVpSGv/0Ip1a/vu3XUq+e6LgAA/IhQCgAAoIzZs2ePrr32Wu3evVvly5dXixYt9OWXX6pbt25Wl4a8zKDIgwHIPUYoBQCwEKEUAABAGfPqq69aXQJO5/hxKS3Ncd0MjnyBUAoAYKEwqwsAAAAAkM/27Y7LhASpYkXfrccMpfbulY4e9d16AAAoBKEUAAAAEGjyHrpns/luPeXLnwq96C0FAPAzQikAAAAg0Gzd6rj05aF7JnMgdUIpAICfEUoBAAAAgcYfg5ybGFcKAGARQikAAAAg0PizpxShFADAIoRSAAAAQKCxoqfUP//4fl0AAORBKAUAAAAEGnpKAQDKAEIpAAAAIJAcOybt3eu4XqeO79eXd6Bzw/D9+gAA+A+hFAAAABBIzF5SFSo4/nytTh3JZnOEYfv2+X59AAD8h1AKAAAACCT+PHRPkqKjpZQUx/Xt2/2zTgAARCgFAAAABBZ/DnJuql3bcUkoBQDwI0IpAAAAIJD4u6eURCgFALAEoRQAAAAQSMxQip5SAIAQRygFAAAABJJt2xyXZlDkD4RSAAALEEoBAAAAgWTHDselP0OpWrVc1w0AgB8QSgEAAACBIitLSk93XDeDIn+gpxQAwAKEUgAAAECg2LnTcRkTIyUl+W+9Zii1e7cjGAMAwA8IpQAAAIBAYR4+V6uWZLP5b72VKzuCMOlUMAYAgI8FdCiVk5Oj++67T/Xq1VNsbKwaNGighx56SIZhOOcxDEOTJk1StWrVFBsbq65du2rjxo0WVg0AAACUUN5Qyp9sNg7hAwD4XUCHUlOnTtXMmTP1/PPPa926dZo6daoef/xxPffcc855Hn/8cU2fPl2zZs3SypUrFRcXpx49eujEiRMWVg4AAACUgFWhlEQoBQDwuwirCyjODz/8oMsvv1y9e/eWJNWtW1fvvPOOfvrpJ0mOXlLTpk3Tvffeq8svv1yS9MYbb6hq1ar66KOPNGjQIMtqBwAAADxGKAUAKEMCuqdUu3bt9PXXX2vDhg2SpN9++03fffedevbsKUnasmWL0tLS1LVrV+djypcvrwsuuEArVqywpGYAAACgxKwMpcx1mjUAAOBjAd1TasKECcrIyFCTJk0UHh6unJwcPfLIIxoyZIgkKS0tTZJUtWpVl8dVrVrVeV9hsrKylJXnrCIZGRmSJLvdLrvd7pXazeV4a3mhju3lGV9ur8jI/Ovy+ioswWvMM2wvz7HNPBNs2ytY6kQIoKcUAKAMCehQ6r333tPbb7+tuXPn6qyzztKaNWs0duxYVa9eXUOHDi3xcqdMmaLJkycXmL548WKVK1euNCUXkJqa6tXlhTq2l2d8sb3yv7U+/9zrq7AUrzHPsL08xzbzTLBsr8zMTKtLQFlBKAUAKEMCOpS64447NGHCBOfYUM2bN9e2bds0ZcoUDR06VCkpKZKk9PR0VatWzfm49PR0tWzZssjlTpw4UePHj3fezsjIUK1atdS9e3clJiZ6pXa73a7U1FR169ZNkfm7nqAAtpdnfLm9Bg50vT1vnlcXbxleY55he3mObeaZYNteZq9qwKcyM6UDBxzXrQ6lDMNxRj4AAHwooEOpzMxMhYW5DnsVHh6u3NxcSVK9evWUkpKir7/+2hlCZWRkaOXKlbrpppuKXG50dLSio6MLTI+MjPT6jrEvlhnK2F6e8cX2yn+ESqg1B68xz7C9PMc280ywbK9gqBEhwOwllZAglS/v//WbQdjRo9KhQ1LFiv6vAQBQpgR0KNWnTx898sgjql27ts466yz9+uuvevrpp3XddddJkmw2m8aOHauHH35YjRo1Ur169XTfffepevXq6tu3r7XFAwAAAJ4wD5uzopeUJMXGSpUrS/v2OWohlAIA+FhAh1LPPfec7rvvPt18883as2ePqlevrv/973+aNGmSc54777xTx44d08iRI3Xo0CF16NBBixYtUkxMjIWVAwAAAB6ycjwpU61ajlDq33+ls8+2rg4AQJkQ0KFUQkKCpk2bpmnTphU5j81m04MPPqgHH3zQf4UBAAAA3hYIoVSNGtKvv0o7d1pXAwCgzAg7/SwAAAAAfC5QQimJUAoA4BeEUgAAAEAgMEMp8yx4ViCUAgD4EaEUAAAAEAgCoadUzZqOy3//ta4GAECZQSgFAAAAWM0wAiOUoqcUAMCPCKUAAAAAqx0+LB096rhu9layAqEUAMCPCKUAAAAAq+3a5bisWFEqV866OsxQ6uBBKTPTujoAAGUCoRQAAEAZMmXKFJ133nlKSEhQlSpV1LdvX61fv97qsmD2TKpe3do6ypeX4uIc1+ktBQDwMUIpAACAMmTp0qUaNWqUfvzxR6Wmpsput6t79+46duyY1aWVbWZPKbOnklVsNg7hAwD4TYTVBQAAAMB/Fi1a5HJ7zpw5qlKlilavXq1OnTpZVBWcoZTVPaUkRyi1YQOhFADA5+gpBQAAUIYdPnxYklSpUiWLKynjzADI6p5SeWv4919r6wAAhDx6SgEAAJRRubm5Gjt2rNq3b69mzZoVOV9WVpaysrKctzMyMiRJdrtddrvd63WZy/TFsgNV+L//KkxSTtWqyrX4eYdVq6ZwSTk7dhRZS1lso2BEOwUH2inw0Uaec3dbEUoBAACUUaNGjdIff/yh7777rtj5pkyZosmTJxeYvnjxYpXz4ZniUlNTfbbsQNNx3TpVkvTzrl1K+/xzS2upd+iQWkhKX71aq05TS1lqo2BGOwUH2inw0Ubuy3TzDK6EUgAAAGXQ6NGj9emnn2rZsmWqWbNmsfNOnDhR48ePd97OyMhQrVq11L17dyUmJnq9NrvdrtTUVHXr1k2RkZFeX34gihg9WpLU+rLLZJx7rqW12E6elF5+WSm5uerVq1eh85TFNgpGtFNwoJ0CH23kObNX9ekQSgEAAJQhhmHolltu0Ycffqhvv/1W9erVO+1joqOjFR0dXWB6ZGSkT3fOfb38gJGbK+3eLUmKqF1bsvo516kjSQrbuVNhp6mlzLRRkKOdggPtFPhoI/e5u50IpQAAAMqQUaNGae7cufr444+VkJCgtLQ0SVL58uUVGxtrcXVl1J49Uk6OFBYmVa1qdTWS2XMuLc1RV3i4tfUAAEIWZ98DAAAoQ2bOnKnDhw+rc+fOqlatmvNv3rx5VpdWdu3a5bisWlWKCIDfjKtWdQRROTlSerrV1QAAQlgAfOsBAADAXwzDsLoE5GeGUtWrW1uHKTxcSkmRdu6U/v03cOoCAIQcekoBAAAAVtq503FZo4a1deRl1mLWBgCADxBKAQAAAFYKtJ5SEqEUAMAvCKUAAAAAKwViTylzsHNCKQCADxFKAQAAAFYK5J5S//5rbR0AgJBGKAUAAABYKRBDqWrVHJe7d1tbBwAgpBFKAQAAAFYKxMP3zICMUAoA4EOEUgAAAIBVsrKkffsc1+kpBQAoYwilAAAAAKuYoU90tFSpkrW15GWGUgcPSidOWFsLACBkEUoBAAAAVsk7npTNZm0teVWs6AjKJCktzdpaAAAhi1AKAAAAsIoZSgXSeFKSIyBLSXFcN2sEAMDLCKUAAAAAq5iDnAfSeFImBjsHAPgYoRQAAABglbyH7wUaBjsHAPgYoRQAAABgFbOnVKAdvicRSgEAfI5QCgAAALAKPaUAAGUYoRQAAABglUAd6Fw6FZQx0DkAwEcIpQAAAACrmL2QzDPdBRJ6SgEAfIxQCgAAALBCZqaUkeG4bgZAgYRQCgDgY4RSAAAAgBXS0x2XsbFSQoK1tRTGDKX27pXsdmtrAQCEJEIpAAAAwAppaY7LlBTJZrO2lsJUrixFRDiumwEaAABe5HEo9frrr+uzzz5z3r7zzjtVoUIFtWvXTtu2bfNqcQAAAEDIyhtKBaKwsFO1Mdg5AMAHPA6lHn30UcXGxkqSVqxYoRkzZujxxx9X5cqVNW7cOK8XCAAAAIQks/dR1arW1lEcxpUCAPhQhKcP2LFjhxo2bChJ+uijj9SvXz+NHDlS7du3V+fOnb1dHwAAABCaAr2nlEQoBQDwKY97SsXHx2v//v2SpMWLF6tbt26SpJiYGB0/fty71QEAAAChilAKAFDGedxTqlu3brr++uvVqlUrbdiwQb169ZIk/fnnn6pbt6636wMAAABCUzCEUtWrOy4JpQAAPuBxT6kZM2aobdu22rt3rxYsWKCkpCRJ0urVq3X11Vd7vUAAAAAgJAVDKGX2lGKgcwCAD3jcU6pChQp6/vnnC0yfPHmyVwoCAAAAyoRgCqXoKQUA8AGPe0pJ0vLly3XNNdeoXbt22rlzpyTpzTff1HfffefV4gAAAICQZBiEUgCAMs/jUGrBggXq0aOHYmNj9csvvygrK0uSdPjwYT366KNeLxAAAAAIOYcPS//tR6tqVWtrKY4ZSqWnSzk51tYCAAg5HodSDz/8sGbNmqWXX35ZkZGRzunt27fXL7/84tXiAAAAgJBk9pKqUEGKibG0lGJVqSKFhUm5udLevVZXAwAIMR6HUuvXr1enTp0KTC9fvrwOHTrkjZoAAACA0BYMh+5JUkSEI5iSGOwcAOB1HodSKSkp2rRpU4Hp3333nerXr++VogAAAICQFiyhlMS4UgAAn/E4lLrhhht06623auXKlbLZbNq1a5fefvtt3X777brpppt8USMAAAAQWsxQKpDHkzIRSgEAfCTC0wdMmDBBubm56tKlizIzM9WpUydFR0fr9ttv1y233OKLGgEAAIDQkp7uuKSnFACgDPM4lLLZbLrnnnt0xx13aNOmTTp69KiaNm2q+Ph4X9QHAAAAhJ5gOnyvenXHJaEUAMDLPA6lTFFRUWratKk3awEAAADKhmAKpcxDDM3eXQAAeIlbodSVV17p9gI/+OCDEhcDAAAA31u2bJmeeOIJrV69Wrt379aHH36ovn37Wl1W2RJMoZRZo1kzAABe4lYoVb58eV/XAQAAAD85duyYzj77bF133XUe/fgILyKUAgDAvVBq9uzZvq4DAAAAftKzZ0/17NnT6jLKrpwcac8ex/VgC6UMQ7LZrK0HABAywjx9wJYtW7Rx48YC0zdu3KitW7d6oyYAAAAgdO3bJ+XmSmFhUnKy1dWcnjmmVGamdPSotbUAAEKKxwOdDxs2TNddd50aNWrkMn3lypV65ZVX9O2333qrNgAAAASArKwsZWVlOW9nZGRIkux2u+x2u9fXZy7TF8sOCDt2KFKSkZys7NxcR0AVyKKjFREXJ9uxY7L/+6/UsGHot1GIoJ2CA+0U+Ggjz7m7rTwOpX799Ve1b9++wPQ2bdpo9OjRni4OAAAAAW7KlCmaPHlygemLFy9WuXLlfLbe1NRUny3bSsm//qp2kjJiY/Xt559bXY5buiQkKP7YMf340Uc6kOcM3KHaRqGGdgoOtFPgo43cl5mZ6dZ8HodSNptNR44cKTD98OHDysnJ8XRxAAAACHATJ07U+PHjnbczMjJUq1Ytde/eXYmJiV5fn91uV2pqqrp166bIyEivL99qtn37JEkJZ5yhXr16WVyNe8Lr15fS0tS2Xj0ZvXqFfBuFCtopONBOgY828pzZq/p0PA6lOnXqpClTpuidd95ReHi4JCknJ0dTpkxRhw4dPF0cAAAAAlx0dLSio6MLTI+MjPTpzrmvl2+Z/0KpsJQUhQXL86tWTZIUsW+flKfmkG2jEEM7BQfaKfDRRu5zdzt5HEpNnTpVnTp1UuPGjdWxY0dJ0vLly5WRkaFvvvnG08UBAADAz44ePapNmzY5b2/ZskVr1qxRpUqVVLt2bQsrKyPS0hyXwXDmPVPeM/ABAOAlHp99r2nTplq7dq0GDBigPXv26MiRI7r22mv1999/q1mzZr6oEQAAAF70888/q1WrVmrVqpUkafz48WrVqpUmTZpkcWVlRHq64zKYQinzDHxm7QAAeIHHPaUkqXr16nr00Ue9XQsAAAD8oHPnzjIMw+oyyi56SgEAIMnNUGrt2rVq1qyZwsLCtHbt2mLnbdGihVcKAwAAAEISoRQAAJLcDKVatmyptLQ0ValSRS1btpTNZiv01zWbzcYZ+AAAAIDiEEoBACDJzVBqy5YtSk5Odl4HAAAAUAJZWdLBg47rwRhKpadLHPoJAPASt0KpOnXqOK9v27ZN7dq1U0SE60Ozs7P1ww8/uMwLAAAAIA9zoPCoKKlCBUtL8UiVKo5Lu90RqiUkWFsPACAkeHz2vYsuukgHDhwoMP3w4cO66KKLvFJUXjt37tQ111yjpKQkxcbGqnnz5vr555+d9xuGoUmTJqlatWqKjY1V165dtXHjRq/XAQAAAJRa3kP3bDZra/FEdLRUsaLjOofwAQC8xONQyjAM2Qr5At2/f7/i4uK8UpTp4MGDat++vSIjI/XFF1/or7/+0lNPPaWK5heipMcff1zTp0/XrFmztHLlSsXFxalHjx46ceKEV2sBAAAASi0Yx5MyMa4UAMDL3Dp8T5KuvPJKSY7BzIcNG6bo6GjnfTk5OVq7dq3atWvn1eKmTp2qWrVqafbs2c5p9erVc143DEPTpk3Tvffeq8svv1yS9MYbb6hq1ar66KOPNGjQIK/WAwAAAJSKGehUrWptHSWRkiKtW0coBQDwGrdDqfLly0tyBEEJCQmKjY113hcVFaU2bdrohhtu8Gpxn3zyiXr06KGrrrpKS5cuVY0aNXTzzTc717NlyxalpaWpa9euLnVecMEFWrFiRZGhVFZWlrKyspy3MzIyJEl2u112u90rtZvL8dbyQh3byzO+3F6RkfnX5fVVWILXmGfYXp5jm3km2LZXsNSJIBAKPaXMcbEAACglt0Op2bNny/jvTBvPPfec4uPjfVaU6Z9//tHMmTM1fvx43X333Vq1apXGjBmjqKgoDR06VGn/falXzfdLU9WqVZ33FWbKlCmaPHlygemLFy9WuXLlvPocUlNTvbq8UMf28owvttfQoa63P//c66uwFK8xz7C9PMc280ywbK/MzEyrS0CoCOZQytznpqcUAMBL3A6lJEcvqbffflt33323GjVq5KuanHJzc3Xuuefq0UcflSS1atVKf/zxh2bNmqWh+f9z9sDEiRM1fvx45+2MjAzVqlVL3bt3V2JiYqnrlhy/qKampqpbt26KzN/1BAWwvTzjy+01cKDr7XnzvLp4y/Aa8wzby3NsM88E2/Yye1UDpRbMoRRjSgEAvMyjUCosLEyNGjXS/v37/RJKVatWTU2bNnWZduaZZ2rBggWSpJT/vhjT09NVrVo15zzp6elq2bJlkcuNjo52GRPLFBkZ6fUdY18sM5SxvTzji+2V/wiVUGsOXmOeYXt5jm3mmWDZXsFQI4KEeegboRQAAJ6ffe+xxx7THXfcoT/++MMX9bho37691q9f7zJtw4YNqlOnjiTHoOcpKSn6+uuvnfdnZGRo5cqVatu2rc/rAwAAADxCTykAAJw86iklSddee60yMzN19tlnKyoqymXAc0k6cOCA14obN26c2rVrp0cffVQDBgzQTz/9pJdeekkvvfSSJMeZAMeOHauHH35YjRo1Ur169XTfffepevXq6tu3r9fqAAAAAErNMEIjlGKgcwCAl3gcSk2bNs0HZRTuvPPO04cffqiJEyfqwQcfVL169TRt2jQNGTLEOc+dd96pY8eOaeTIkTp06JA6dOigRYsWKSYmxm91AgAAeMJutystLU2ZmZlKTk5WpUqVrC4J/nD0qGQOmp/vRD1Bwax5714pJ8faWgAAIcHjUKo0A4yXxKWXXqpLL720yPttNpsefPBBPfjgg36sCgAAwDNHjhzRW2+9pXfffVc//fSTTp48KcMwZLPZVLNmTXXv3l0jR47UeeedZ3Wp8BWzl1RCghQXZ20tJZGcLIWFSbm5jmAKAIBS8nhMqbxOnDihjIwMlz8AAAC4evrpp1W3bl3Nnj1bXbt21UcffaQ1a9Zow4YNWrFihe6//35lZ2ere/fuuuSSS7Rx40arS4YvBPOhe5IUHu4IpiTGlQIAeIXHPaWOHTumu+66S++99572799f4P4cuvICAAC4WLVqlZYtW6azzjqr0PvPP/98XXfddZo5c6bmzJmj5cuX++VMx/CzYA+lJEft6emyMa4UAMALPA6l7rzzTi1ZskQzZ87U//3f/2nGjBnauXOnXnzxRT322GO+qBEAACCovfPOO27NFxMToxtvvNHH1cAyZigVjONJmVJSpN9+cwx2Xrmy1dUAAIKcx6HUwoUL9cYbb6hz584aPny4OnbsqIYNG6pOnTp6++23XQYhBwAAQEEnTpzQ2rVrtWfPHuXm5rrcd9lll1lUFXwuFHpK/Reo2QilAABe4HEodeDAAdWvX1+SlJiYqAMHDkiSOnTooJtuusm71QEAAISYRYsW6dprr9W+ffsK3Gez2RgKIZSFQihl1p6eLhVxOCoAAO7yeKDz+vXra8uWLZKkJk2a6L333pPk6EFVoUIFrxYHAAAQam655RZdddVV2r17t3Jzc13+CKRCXAiFUjYGOgcAeIHHodTw4cP122+/SZImTJigGTNmKCYmRuPGjdMdd9zh9QIBAABCSXp6usaPH6+qwTyuEErGHBw8BEIpMdA5AMALPD58b9y4cc7rXbt21d9//63Vq1erYcOGatGihVeLAwAACDX9+/fXt99+qwYNGlhdCvwtlHpKEUoBALzA7VAqNzdXTzzxhD755BOdPHlSXbp00f333686deqoTp06vqwRAAAgZDz//PO66qqrtHz5cjVv3lyRkZEu948ZM8aiyuBTubmh0VPK7OFHKAUA8AK3Q6lHHnlEDzzwgLp27arY2Fg9++yz2rNnj1577TVf1gcAABBS3nnnHS1evFgxMTH69ttvZbPZnPfZbDZCqVB14ICUne24XqWKtbWUhtlT6uBBhdntFhcDAAh2bodSb7zxhl544QX973//kyR99dVX6t27t1555RWFhXk8NBUAAECZdM8992jy5MmaMGEC+1BliXnoXuXKUr7ecUGlYkVH/Xa7og8dsroaAECQc3tPaPv27erVq5fzdteuXWWz2bRr1y6fFAYAABCKTp48qYEDBxJIlTWhMJ6UJNlszucQffCgxcUAAIKd23tD2dnZiomJcZkWGRkpO912AQAA3DZ06FDNmzfP6jLgb6ESSkmnQil6SgEASsntw/cMw9CwYcMUHR3tnHbixAndeOONiouLc0774IMPvFshAABACMnJydHjjz+uL7/8Ui1atCgw0PnTTz9tUWXwKTOUMgcKD2b/PYcYQikAQCm5HUoNHTq0wLRrrrnGq8UAAACEut9//12tWrWSJP3xxx8u9+Ud9BwhJhR7SnH4HgCglNwOpWbPnu3LOgAAAMqEJUuWWF0CrBCCoRQ9pQAApcUImwAAAH4wadIkrV692uoyYJUQDKXoKQUAKC23e0oBKJv69Ck4beFC/9cBAMHu33//Vc+ePRUVFaU+ffrosssuU5cuXRQVFWV1afCHUAyl6CkFACglekoBAAD4wWuvvaa0tDS98847SkhI0NixY1W5cmX169dPb7zxhg4cOGB1ifCl9HTHJaEUAABOhFIAAAB+EhYWpo4dO+rxxx/X+vXrtXLlSl1wwQV68cUXVb16dXXq1ElPPvmkdu7caXWp8Ca7Xdq3z3E9FEIpzr4HAPASt0Kpc845Rwf/O2b8wQcfVGZmpk+LAgAACDX5z7QnSWeeeabuvPNOff/999qxY4eGDh2q5cuX65133vF5PTNmzFDdunUVExOjCy64QD/99JPP11lm7dnjuIyIkCpVsrYWb/gvWIs4cUI6etTiYgAAwcytUGrdunU6duyYJGny5Mk6ypcPAACAR1q0aKELLrhAL7/8so4cOVLg/uTkZI0YMUIff/yxbr/9dp/WMm/ePI0fP17333+/fvnlF5199tnq0aOH9pjhCbzLHE+qalUpLAQOVIiPlxEX57huPjcAAErArYHOW7ZsqeHDh6tDhw4yDENPPvmk4uPjC5130qRJXi0QAAAgFCxdulSzZ8/WbbfdpnHjxqlfv366/vrr1bFjR7/X8vTTT+uGG27Q8OHDJUmzZs3SZ599ptdee00TJkzwez0hL5QGOTelpEibN8uWni6deabV1QAAgpRbodScOXN0//3369NPP5XNZtMXX3yhiIiCD7XZbIRSAAAAhejYsaM6duyo5557Tu+9957mzJmjCy+8UA0bNtSIESM0dOhQpfghtDh58qRWr16tiRMnOqeFhYWpa9euWrFihc/Xf1pr1ihs/nzVPnxY6tXL6mq8I29PqRBhVK0q2+bNodVTavNm6a23HGOAhYiwnBw12bxZYT/+KIWHW10OikA7Bb6QbqNhw6SGDS1bvVuhVOPGjfXuu+9Kcuy0fP3116pSpYpPCwMAAAhFcXFxGj58uIYPH65NmzZp9uzZmjFjhu677z5dcskl+uSTT3y6/n379iknJ0dV8wUkVatW1d9//13oY7KyspSVleW8nZGRIUmy2+2ye/kfeNuaNYp45BHVbNHC68u2StjOnQqXlFulinJC5DnZqlRRmKTc3btDpp3Cx41T2MKFVpfhVeGSGltdBE6Ldgp8odxG2R06yKhTx+vLdfe7wa1QKq/c3FyPiwEAAEBBDRs21N133606depo4sSJ+uyzz6wuqVBTpkzR5MmTC0xfvHixypUr59V1JW/frnaSog8dUmpqqleXbZXmK1eqvqRNR49q3eefW12OVzQ/eVL1JW1ZsUJ/169vdTlecdFvvylR0q42bXQiKcnqcgDAL7b884+O5vnhyVvcPUGex6GUJG3evFnTpk3TunXrJElNmzbVrbfeqgYNGpRkcQAAAGXOsmXL9Nprr2nBggUKCwvTgAEDNGLECJ+vt3LlygoPD1d6errL9PT09CIPH5w4caLGjx/vvJ2RkaFatWqpe/fuSkxM9G6BtWtL99+v6IMH1a1bN0VGRnp3+RYIf+MNSVKD9u1VL0QOSTRWr5Y+/1wN4uJUP0SeU8R/77/kGTOk5s0trsY77Ha7UlNTQ+a9FKpop8AXym1Uy0fLNXtVn47HodSXX36pyy67TC1btlT79u0lSd9//73OOussLVy4UN26dfN0kQAAAGXCrl27NGfOHM2ZM0ebNm1Su3btNH36dA0YMEBx5tnMfCwqKkqtW7fW119/rb59+0py9IT/+uuvNXr06EIfEx0drejo6ALTIyMjvb9zXsuxexx95Ijs/60j6P13VsPwGjUUHgrPR1J29eqSpLA9exQWCs/p5Elp/35JUmTt2lIoPKc8fPJehdfRToGPNnKfu9vJ41BqwoQJGjdunB577LEC0++66y5CKQAAgEL07NlTX331lSpXrqxrr71W1113nRo3tmaEivHjx2vo0KE699xzdf7552vatGk6duyY82x8lqpUSUZEhGzZ2Y4wp25dqysqvVA8+545Jlm+HndBy3wekZESh+4BgN94HEqtW7dO7733XoHp1113naZNm+aNmgAAAEJOZGSk5s+fr0svvVThFp+5Z+DAgdq7d68mTZqktLQ0tWzZUosWLSow+LklwsIcgcfOnY6ggFAqMP33XGyhEkrt3u24TEmRbDZrawGAMsTjUCo5OVlr1qxRo0aNXKavWbOGM/IBAAAUwddn1fPU6NGjizxcz2pG1aqy7dwpmxnmBLNjx6SjRx3XQyiUMvL2lDKM4A9yzFCqWjVr6wCAMsbjUOqGG27QyJEj9c8//6hdu3aSHGNKTZ061WUATAAAADhs375dtWvXdnv+nTt3qkaNGj6sKMCF0qFh5nMoV06Kj7e2Fm/678dom90uHTwoVapkcUGlRCgFAJYI8/QB9913nyZNmqTnnntOF154oS688EI9//zzeuCBB3Tvvff6okYAAICgdt555+l///ufVq1aVeQ8hw8f1ssvv6xmzZppwYIFfqwuAP0XSoVET6m8h+4Fe2+ivKKjdTIhwXE9FNop7+F7AAC/8binlM1m07hx4zRu3DgdOXJEkpRgfiEBAACggL/++kuPPPKIunXrppiYGLVu3VrVq1dXTEyMDh48qL/++kt//vmnzjnnHD3++OPq1auX1SVbygilnlKhOJ7Uf7LKl1fUkSOO59i0qdXllA49pQDAEh73lMorISGBQAoAAOA0kpKS9PTTT2v37t16/vnn1ahRI+3bt08bN26UJA0ZMkSrV6/WihUrynwgJenUINqh0APHfA6BMIi8l52oWNFxJRTaiVAKACzhcU8pAAAAlExsbKz69++v/v37W11KQKOnVHDIqlDBcYVQCgBQQqXqKQUAAAB4ndlTilAqoNFTCgBQWoRSAAAACCj0lAoOIdNTKifn1GuNUAoA/MqjUMput6tLly7O8Q8AAAAArzN7Sh05Ih07ZnExpRTKoZTZUyrYw8P9+x3BlM0WkmN/AUAg8yiUioyM1Nq1a31VCwAAACDFxys7KspxPdgDjxAOpU6ESk8p89C95GQpgiF3AcCfPD5875prrtGrr77qi1oAAADKnF9++cXqEgKPzXaqF04wBx6GEdKhVMgcvsd4UgBgGY9/CsjOztZrr72mr776Sq1bt1ZcXJzL/U8//bTXigMAAAh1559/vsaMGeOyD/X555+rV69eFlZlvawKFRSXnh7cgcfBg5Ld7rgegoeFOYPDvXul7Ozg7WVkhlIhGBwCQKDz+Jvjjz/+0DnnnCNJ2rBhg8t9NpvNO1UBAACUEc2bN1diYqKGDx+u2bNnS5LuvffeMh9KhcSZ3cxDDytWlKKjra3FB7ISEmSEhcmWm+sIpoK1pxE9pQDAMh6HUkuWLPFFHQAAAGWSzWbTAw88oGnTpql///565513ZBiG1WVZLiQODQvhQ/ckSeHhUpUqjueZlha8oQ6hFABYpsR9bDdt2qTNmzerU6dOio2NlWEY9JQCAADwUGJioiRp7Nixqlixoi677DIdP37c4qqsFxI9pUI9lJIchyWaoVSwIpQCAMt4PND5/v371aVLF51xxhnq1auXdv/3IT5ixAjddtttXi8QAAAgFAwbNkyZmZkFpn/77bfO60OHDtXIkSO1Z88eP1YWmJw9pYL57HtmUBOC40mZDDNwC+Z2IpQCAMt4HEqNGzdOkZGR2r59u8qVK+ecPnDgQC1atMirxQEAAISKN998U0ePHnXevummm3To0CGXebKzs3XFFVfowIEDfq4u8ITE2ffKSk8pKTTaiVAKAPzO41Bq8eLFmjp1qmrWrOkyvVGjRtq2bZvXCgMAAAgl+ceJevvtt13Cp/T0dOehfAixMaVCuadUlSqOK8HaToZRNsJDAAhQHodSx44dc+khZTpw4ICiQ/CsIgAAAL5Q2GDmJ06csKCSwHQibygVrAO/l4UeOGaQE6yh1NGjknlYbQiHhwAQqDwOpTp27Kg33njDedtmsyk3N1ePP/64LrroIq8WBwAAUJZw0phTnD2lTp6U8h3mGDTKQChlBPvhe2bd8fGOPwCAX3l89r3HH39cXbp00c8//6yTJ0/qzjvv1J9//qkDBw7o+++/90WNAAAAIWHu3Lnq1KmTmjdvbnUpAS83KkpGhQqyHTrkCA7MMaaCSVk4LCzYe0qVhTYCgADmcSjVrFkzbdiwQc8//7wSEhJ09OhRXXnllRo1apSqhfCvQAAAAKXRsWNH3X///Tpy5IgiIyOVnZ2t+++/X+3bt1fLli2VnJxsdYmBp2pVRy+ptDTpzDOtrsYz2dnS3r2O6yEceIRMT6kQbiMACGQeh1KSVL58ed1zzz3ergUAACBkLV26VJK0ceNGrV69Wr/88ot++eUX3X333Tp06BCH7hXCSEmRbf364Aw89uxxjIUVHi4lJVldje+YYc7hw9KJE1JMjLX1eIpQCgAsVaJQ6uDBg3r11Ve1bt06SVLTpk01fPhwVapUyavFAQAAhJpGjRqpUaNGGjRokHPali1b9PPPP+vXX3+1sLIAFMy9cMyaq1RxBFOhqnx5KTpaysqS0tOlOnWsrsgzhFIAYCmPBzpftmyZ6tatq+nTp+vgwYM6ePCgpk+frnr16mnZsmW+qBEAACCk1atXT1dddZUeffRRq0sJKIYZFKSnW1tISZSVsMNmC43wkGFIAMASHveUGjVqlAYOHKiZM2cq/L9ffXJycnTzzTdr1KhR+v33371eJAAAAMqgKlUcl8EcdoR6KCU5nuP27bQTAMBjHveU2rRpk2677TZnICVJ4eHhGj9+vDZt2uTV4gAAAFB2GcF8ZreyFHbQTgCAEvI4lDrnnHOcY0nltW7dOp199tleKQoAAAAIicPCykLYQSgFACghtw7fW7t2rfP6mDFjdOutt2rTpk1q06aNJOnHH3/UjBkz9Nhjj/mmSgAAAJQ5BqFUcAjWUCo399R4ZWWhnQAgALkVSrVs2VI2m02GYTin3XnnnQXmGzx4sAYOHOi96gAAAFB2mUHB3r1STk5wncWuLA2gHayh1L59jteVzSYlJ1tdDQCUSW6FUlu2bPF1HQAAAICr5GQpLMzRo2Xv3uDqzbJ7t+MymGouqWA9S6IZolWuLEVGWlsLAJRRboVSderU8XUdAAAAgKvwcEcwlZ7uCBCCKeApS4fvBethlmWpjQAgQLkVSuW3a9cufffdd9qzZ49yc3Nd7hszZoxXCgMAAACUkuIIpYKpF87Ro44/qWwEHnkP3zMMx+FwwYBQCgAs53EoNWfOHP3vf/9TVFSUkpKSZMvzpWOz2QilgDKgT5+C0xYu9H8dAIAyIBh74ZgBWrlyUny8tbX4g9lGx49LR45IiYnW1uMuQikAsJzHodR9992nSZMmaeLEiQoLC/NFTQAAAIBDMA6inTfsCJZeQ6URFyclJDgCqbQ0QikAgNs8TpUyMzM1aNAgAikAAAD4XrCHUmUF7QQAKAGPk6URI0bo/fff90UtAAAA8LFHHnlE7dq1U7ly5VShQgWryzk9wo7gEMztVK2atXUAQBnmcSg1ZcoULV26VJ07d9Ytt9yi8ePHu/z50mOPPSabzaaxY8c6p504cUKjRo1SUlKS4uPj1a9fP6UH00CYAAAAfnTy5EldddVVuummm6wuxT3BHHaUxVAqmPbDy2I7AUCA8XhMqSlTpujLL79U48aNJanAQOe+smrVKr344otq0aKFy/Rx48bps88+0/vvv6/y5ctr9OjRuvLKK/X999/7rBYAAIBgNXnyZEmOk9cEBUKp4BCMA9KXxXYCgADjcSj11FNP6bXXXtOwYcN8UE7hjh49qiFDhujll1/Www8/7Jx++PBhvfrqq5o7d64uvvhiSdLs2bN15pln6scff1SbNm38ViMAAECoysrKUlZWlvN2RkaGJMlut8tut3t9feYy7Xa7lJSkSElGWpqyfbAuXwjftUthkrKrVJERJDV7yqWNJIUlJytcUu6uXcoJhueclaXIgwclSfakJCkYai6B/O2EwEQ7BT7ayHPubiuPQ6no6Gi1b9/e44JKY9SoUerdu7e6du3qEkqtXr1adrtdXbt2dU5r0qSJateurRUrVhQZSvljx4oXrWfYXp7x5faKjCzZ4wK96XiNeYbt5Tm2mWeCbXsFS52+MmXKFGcPq7wWL16scuXK+Wy9qampijx6VL0k2Q4d0qKPP1ZuSb+o/OjC9etVQdLPO3Yo/fPPrS7Hp1JTUyVJtffsUStJe37/XSuD4DnH7t2r7pJyIiL0+Q8/hPxZEs12QmCjnQIfbeS+zMxMt+azGYZheLLgKVOmaPfu3Zo+fXqJCvPUu+++q0ceeUSrVq1STEyMOnfurJYtW2ratGmaO3euhg8f7hIwSdL555+viy66SFOnTi10mQ888EChO1Zz58716Y4VAAAITpmZmRo8eLAOHz6sxAA83f2ECROK3O8xrVu3Tk2aNHHenjNnjsaOHatDhw6ddvmF/aBXq1Yt7du3zyfbw263KzU1Vd26dVNkRIQiEhJkO3lS9k2bpNq1vb4+b4uoV0+2nTuVvWKFjNatrS7HJ1zaKDJSts8/V0TfvjJatVL2ypVWl3datlWrFNG+vYzatZW9aZPV5fhM/nZCYKKdAh9t5LmMjAxVrlz5tPtOHveU+umnn/TNN9/o008/1VlnnVWgQT744APPqy3Cjh07dOuttyo1NVUxMTFeW+7EiRNdBmU3d6y6d+/utR0rXrSeYXt5xpfba+DAkj1u3jyvluF1vMY8w/byHNvMM8G2vcxe1YHqtttuO+3QCvXr1y/x8qOjoxUdHV1gemRkpE/bz7n8qlWlHTsUuX+/1KCBz9bnFbm5zsG+I2rWLHkX5CDhbKOaNSVJtvT0oHhPa98+SZItJSU46i0lX79X4R20U+Cjjdzn7nbyOJSqUKGCrrzySo8LKonVq1drz549Ouecc5zTcnJytGzZMj3//PP68ssvdfLkSR06dMjllMbp6elKKWbAQn/uWPGi9QzbyzO+2F4lPUIlWJqN15hn2F6eY5t5Jli2V6DXmJycrOTkZKvL8J2UFGnHjuAYRPvAASk723G9ShVra/GnvGffy82Vwjw+ybd/Mcg5AAQEj0Op2bNn+6KOQnXp0kW///67y7Thw4erSZMmuuuuu1SrVi1FRkbq66+/Vr9+/SRJ69ev1/bt29W2bVu/1QkAABAstm/frgMHDmj79u3KycnRmjVrJEkNGzZUfHy8tcUVJZjOwGfWmJQkRUVZW4s/mQFcTo4jmKtc2dp6TodQCgACgsehlD8lJCSoWbNmLtPi4uKUlJTknD5ixAiNHz9elSpVUmJiom655Ra1bduWM+8BAAAUYtKkSXr99dedt1u1aiVJWrJkiTp37mxRVacRjKFUWQs7IiMdQdz+/Y5tEOih1O7djsuy1k4AEGA8DqXq1asnWzFnp/jnn39KVZCnnnnmGYWFhalfv37KyspSjx499MILL/i1BgAAgGAxZ84czZkzx+oyPEMoFRxSUk6FUvl+WA44ZbmdACCAeBxKjR071uW23W7Xr7/+qkWLFumOO+7wVl1F+vbbb11ux8TEaMaMGZoxY4bP1w0AAAALEEoFh5QU6c8/g6udqlWztg4AKOM8DqVuvfXWQqfPmDFDP//8c6kLAgAAAFwQSgUH2gkA4CGvnRajZ8+eWrBggbcWBwAAADhUreq4TE+3tg53mGMVlcUeOMESShkGoRQABAivhVLz589XpUqVvLU4AAAAwCFv2GEY1tZyOmU57AiWUCojQzpxwnHdDDwBAJbw+PC9Vq1auQx0bhiG0tLStHfvXgYYBwAAgPeZwUFmpnT0qJSQYG09xSGUCvwebWYblS8vxcZaWwsAlHEeh1J9+/Z1uR0WFqbk5GR17txZTZo08VZdAAAAgEN8vOPv6FFHoEAoFZjM8DDQe0qV5TYCgADjcSh1//33+6IOAAAAoGgpKdKmTY5AoVEjq6spXFaWdOCA43pZDDyC5fA9QikACBheG1MKAAAA8JlgCDz27HFcRkZKFStaW4sVzDbat0+y262tpTiEUgAQMNzuKRUWFuYyllRhbDabsrOzS10UAAAA4CIYQimztipVpLAy+NtvUpIUHi7l5DgCuho1rK6ocOYZEgmlAMBybodSH374YZH3rVixQtOnT1dubq5XigIAAABcmAGCGSgEol27HJfVq1tbh1XCwhzjSu3a5WinQA2lyno7AUAAcTuUuvzyywtMW79+vSZMmKCFCxdqyJAhevDBB71aHAAAACDpVIAQyKGUWVtZDjuqVXOEPoHco412AoCAUaJ+xbt27dINN9yg5s2bKzs7W2vWrNHrr7+uOnXqeLs+AAAA4FSAYPZyCURmbdWqWVuHlcznTjsBANzgUSh1+PBh3XXXXWrYsKH+/PNPff3111q4cKGaNWvmq/oAAACA4AqlynIPHNoJAOABtw/fe/zxxzV16lSlpKTonXfeKfRwPgAAAMAngqEHDoeFBf5hlsePS4cOOa6X5XYCgADhdig1YcIExcbGqmHDhnr99df1+uuvFzrfBx984LXiAASPPn0KTlu40P91AABClBkgHDggnTghxcRYW09h6IET+D2lzLAsNlZKTLS2FgCA+6HUtddeK5vN5staAAAAgMJVrChFR0tZWY5BtOvWtbqighirKPBDqbzBIf/bAIDl3A6l5syZ48MyAAAAgGLYbI4gYcsWR7AQaKGU3S7t3eu4Tk+pwA2lOMQSAAJKic6+BwAAAPhdIAce6emSYUgREVLlylZXYx2zjdLTpexsa2spDL3ZACCgEEoBAAAgOARyKGXWlJIihZXhXezkZCk83BHQpadbXU1BjPsFAAGlDH9jAgAAIKgEcijFYWEOYWGOYE6inQAAp0UoBQAAgOBgHnIViGEHPXBOMbeBGQAFEg7fA4CAQigFAACA4BAMYQehVGD3aKOdACCgEEoBAAAgOARy2GEGZfTACex2IpQCgIBCKAUAAIDgQNgRHAK1nTIzpcOHHdcJDwEgIBBKAQAAIDiYYcehQ46AIZAQSp0SqKGU2ZutXDkpMdHaWgAAkqQIqwsAELr69HG9vXChNXUAAEJEYqIjUMjMdAQMDRpYXdEpHL53SqCGUnmDQ5vN2loAAJLoKQUAAIBgYbMF5hn47HZpzx7HdXpKBW4oRXAIAAGHUAoAAADBIxDPwJeW5riMjJSSkqytJRCYoc/evY7ALlBwiCUABBxCKQAAAASPQOyFY9aSkiKFsXutpCRHQCedCuwCAaEUAAQcvjUBAAAQPAIxlDJ7bRF2OISFBeZhlhy+BwABh1AKAAAAwSMQQyl64BREOwEA3EAoBQAAgOBB2BEcaCcAgBsIpQAAABA8AjHs4LCwgmgnAIAbIqwuAEDZ1qdPwWkLF/q/DgBAkDADhUA6+x49cAoKtFDq2DHp8GHHddoJAAIGPaUAAAAQPMxAISNDOnrU2lpMhFIFmdsiUMJDs464OCkhwdpaAABOhFIAAABlxNatWzVixAjVq1dPsbGxatCgge6//36dPHnS6tLcl5Agxcc7rgda4MFhYacE2tn38raRzWZtLQAAJw7fAwAAKCP+/vtv5ebm6sUXX1TDhg31xx9/6IYbbtCxY8f05JNPWl2e+6pXlzZscAQejRpZW0tWlrR376m64BBoh+/9+6/jskYNa+sAALgglALgN4WNH+XNZTEWFQAU75JLLtEll1zivF2/fn2tX79eM2fODN5QympmDdHRUlKStbUEEjOU2r/fEdxFR1tbjxlK1axpbR0AABeEUgAAAGXY4cOHValSpWLnycrKUlZWlvN2RkaGJMlut8tut3u9JnOZRS07PCVFYZJyduxQrg/W7wnbtm2KkGTUrKns7GxLa/Gn07WR4uMVER0tW1aW7Nu3S3Xr+q+4QoTt2KFwSTnVqln+mvGn07YTAgLtFPhoI8+5u60IpQAAAMqoTZs26bnnnjttL6kpU6Zo8uTJBaYvXrxY5cqV81V5Sk1NLXR60xMn1EjSlu+/15+NG/ts/e6osXy5zpW0PyZG33/+uaW1WKGoNpKkrhUqKC49XT8uWKADZ57px6oKOu/nn1Vd0p+HD2sL7YQARTsFPtrIfZmZmW7NRygFAAAQ5CZMmKCpU6cWO8+6devUpEkT5+2dO3fqkksu0VVXXaUbbrih2MdOnDhR48ePd97OyMhQrVq11L17dyUmJpau+ELY7XalpqaqW7duioyMLHB/2D//SB99pPqRkarTq5fX1++JsL//liRVatFCvSyuxZ9O10aSFN6okZSerra1a8uweNuEP/qoJKlp9+46k3ZCgKGdAh9t5DmzV/XpEEoBCDiMFwUAnrnttts0bNiwYuepX7++8/quXbt00UUXqV27dnrppZdOu/zo6GhFFzImUGRkpE93zotcfp06kqSwnTsVZvU/B/+d1S2sdm3ra7FAsa+BWrUkSRG7d0tWb5udOx211K1rfS0W8PV7Fd5BOwU+2sh97m4nQikAAIAgl5ycrOTkZLfm3blzpy666CK1bt1as2fPVlhYmI+r8wFzsGpz8GorMYB20QKlnbKzneEhZ98DgMBCKAUAAFBG7Ny5U507d1adOnX05JNPau/evc77UlJSLKzMQ//1wNHu3Y7AIcLCXVpCqaKZ7WR1KJWWJuXmOl4nVapYWwsAwAWhFAAAQBmRmpqqTZs2adOmTaqZL0QxDMOiqkqgShVHwJCdLaWnW9v7hVCqaOY22bHD2jrMNqpeXQoPt7YWAICLIOyvDQAAgJIYNmyYDMMo9C+ohIc7AgbJ2sAj72FhhFIFBcrhe/+NJ0UbAUDgIZQCAABA8AmEwIPDwoqX/zBLq9CbDQACFqEUAAAAgk8gjFeU97CwYBww3teqVHGc6S4391SPMisQSgFAwOLbEwAAAMEnEMYrIuwoXljYqfG+AiE85Mx7ABBwGOgcQFDo08fqCgAAASUQDt8jlDq9mjWlrVtpJwBAoegpBQAAgOBDKBUc6NEGACgGoRQAAACCjzmmlJVhB2d1Oz2rx/7KzZV27XJcp50AIOBw+B6AkFHYIX4LF/rucQAAC5kBw65dUk6OFB7u/xrogXN6Vvdo27dPOnlSstmkatWsqQEAUCR6SgEAACD4pKQ4gqicHCk93ZoaCKVOz+rD98w2SklxnAkQABBQCKUAAAAQfMLDperVHdet6IWTm8vhe+6w+vA9zrwHAAGNUAoAAADBycpeOHv3Sna747CwlBT/rz9YmG20e7eUne3/9dObDQACGqEUgJDWp4/jb+BAx23zEgAQAqwcr4jDwtxTpYoUEeE4zDItzf/rJ5QCgIBGKAUAAIDgFAihFGFH8cLDTx06Z0U7mb3oaCcACEiEUgAAAAhO5nhFVhy+t22b47J2bf+vO9hYGR6a7VSnjv/XDQA4LUIpAAAABCfCjuBgZXi4fbvjkvAQAAJShNUFAIC/9elTsnkWLvR+LQCAUrAylDLDDkKp07OqnbKzT62TdgKAgERPKQAAAAQnswfOzp2OgbT9icP33GfVWRJ373a8LiIjpWrV/LtuAIBbCKUAAAAQnKpVc5zZLTtb2rXLv+vm8D33mdvI3Gb+Yq6vZk0pjH97ACAQ8ekMAACA4BQefqqn0tat/lvv8ePSnj2O64RSp2d1KEUbAUDAIpQCAABA8LIi8DAPQ4uLkypW9N96g1Xduo7L9HRHoOcvjPsFAAGPUAoAAADBywwc/NlTKm8PHJvNf+sNVhUqSAkJjuv+DA8Z9wsAAh6hFAAAAIKX2QvHirCDHjjusdloJwBAoQI6lJoyZYrOO+88JSQkqEqVKurbt6/Wr1/vMs+JEyc0atQoJSUlKT4+Xv369VN6erpFFQMAAMCvrDh8zzwsjB447rOiRxvtBAABL6BDqaVLl2rUqFH68ccflZqaKrvdru7du+vYsWPOecaNG6eFCxfq/fff19KlS7Vr1y5deeWVFlYNoCzr06fgHwDAh8weOFYdvgf3+LunlGHQTgAQBCKsLqA4ixYtcrk9Z84cValSRatXr1anTp10+PBhvfrqq5o7d64uvvhiSdLs2bN15pln6scff1SbNm2sKBsAAAD+YgYO27dLublSmB9+cyXs8Jy/e0odPCiZP2TXquWfdQIAPBbQPaXyO3z4sCSpUqVKkqTVq1fLbrera9euznmaNGmi2rVra8WKFZbUCAAAAD+qWdMRRGVlOc7u5g+c1c1z/u7RZgaHVapIsbH+WScAwGMB3VMqr9zcXI0dO1bt27dXs2bNJElpaWmKiopShQoVXOatWrWq0tLSilxWVlaWsrKynLczMjIkSXa7XXa73Sv1msvx1vJCHdvLM77cXpGRXl9kQIiMtLtcloQ7m7uw7ReML2vek55jm3km2LZXsNRZJkVGSjVqSDt2OIKIatV8u76cHMe6JMYq8oS/x/6iNxsABIWgCaVGjRqlP/74Q999912plzVlyhRNnjy5wPTFixerXLlypV5+XqmpqV5dXqhje3nGF9tr6FCvLzKgDB5c8m32+eenn6ew7efO4wIV70nPsc08EyzbKzMz0+oSUJw6dRxB0datkq+Hb9i9W8rOliIipOrVfbuuUGL2lNq1y9GrLTrat+ujNxsABIWgCKVGjx6tTz/9VMuWLVPNmjWd01NSUnTy5EkdOnTIpbdUenq6UlJSilzexIkTNX78eOftjIwM1apVS927d1diYqJXarbb7UpNTVW3bt0UGapdT7yI7eUZX26vgQO9uriAERlp1+DBqZo7t5vsdv++xubN8+vqvIL3pOfYZp4Jtu1l9qpGgKpbV/ruO//0wjHDjpo1pfBw368vVFSuLJUrJ2VmOgLEhg19uz7ztUBvNgAIaAEdShmGoVtuuUUffvihvv32W9WrV8/l/tatWysyMlJff/21+vXrJ0lav369tm/frrZt2xa53OjoaEUX8utMZGSk13eMfbHMUMb28owvtleoH6Fit0f6PZQK5pc070nPsc08EyzbKxhqLNP8eWiYOSYSYYdnbDZHO61b59iGvg6lzHaipxQABLSADqVGjRqluXPn6uOPP1ZCQoJznKjy5csrNjZW5cuX14gRIzR+/HhVqlRJiYmJuuWWW9S2bVvOvAcAAFBW+HMQ7X/+cVzWr+/7dYWaunVPhVK+ZrZTgwa+XxcAoMQCOpSaOXOmJKlz584u02fPnq1hw4ZJkp555hmFhYWpX79+ysrKUo8ePfTCCy/4uVIAKFqfPgWnLVzo/zoAIGT5s6cUYUfJ+audDIPwEACCRECHUoZhnHaemJgYzZgxQzNmzPBDRQAAAAg4eXtKGYbjUDFfIewoOX/1aDtwQDLHgTPXCQAISGFWFwAAAACUijm+U2amtG+fb9dFKFVyZk8pX4dSZhtVry7Fxvp2XQCAUiGUAgAAQHCLjnacDU+SNm/23XqysqR//3VcJ5TynHnSIjM08hXzNUAbAUDAI5QCAABA8DPHePJlKGUeHhgXJyUn+249oco8496uXY5ebb7CuF8AEDQIpQAAAMqQyy67TLVr11ZMTIyqVaum//u//9OuXbusLqv0zMBj0ybfrSNv2OHLcatCVaVKUoUKjuu+7C3FIZYAEDQIpQAAAMqQiy66SO+9957Wr1+vBQsWaPPmzerfv7/VZZWe2SvGH6EUYUfJ2Gz+6dFGOwFA0Ajos+8BAADAu8aNG+e8XqdOHU2YMEF9+/aV3W5XZGSkhZWVktlTirAjsDVsKK1eTXgIAJBEKAUAlujTp+C0hQv9XweAsu3AgQN6++231a5du2IDqaysLGVlZTlvZ2RkSJLsdrvsdrvX6zKX6dGy69RRpCRj0yZl+6AmSQrftElhknLq1FGuj9YRLErURpLC6tZVuKScDRt8sw1PnlTEjh2ySbLXqiXRTi6XCEy0U+CjjTzn7rYilAIAAChj7rrrLj3//PPKzMxUmzZt9OmnnxY7/5QpUzR58uQC0xcvXqxy5cr5qkylpqa6PW/EsWPqLcm2d68Wz5+vbB/U1XntWpWX9NO+fdrz+edeX34w8qSNJKl2ZqZaSdq/cqVW+GAbxu3era65ucqOitLnq1cz9td/PG0nWIN2Cny0kfsy3TyhBaEUAABAkJswYYKmTp1a7Dzr1q1TkyZNJEl33HGHRowYoW3btmny5Mm69tpr9emnn8pWxD/wEydO1Pjx4523MzIyVKtWLXXv3l2JiYneeyL/sdvtSk1NVbdu3Tw6pNC49VbZ9u1T9wYNpFatvFuUYShiyBBJ0rkDBkiNG3t3+UGmpG1kS0yUnntOyRkZ6tWrl9frsi1eLEkKb9hQvXr39vryg01J2wn+RTsFPtrIc2av6tMhlAIAAAhyt912m4YNG1bsPPXzjK9TuXJlVa5cWWeccYbOPPNM1apVSz/++KPatm1b6GOjo6MVHR1dYHpkZKRPd849Xn7DhtK+fYrcvl06/3zvFrNnj3TsmGSzKbJRI4l/SiSVoI3+C/Ns27Yp0jCkqCjvFrR9u2P5DRrwj2Mevn6vwjtop8BHG7nP3e1EKAUAABDkkpOTlZycXKLH5ubmSpLLmFFBq0ED6ccffTOI9saNjstataRCAjq4qVo1KTZWOn5c2rZNatTIu8vfsMFx6e3lAgB8IszqAgAAAOAfK1eu1PPPP681a9Zo27Zt+uabb3T11VerQYMGRfaSCiq+PAPf+vWOyzJ+2F6p2WyO8FDyTXhohlK0EwAEBUIpAACAMqJcuXL64IMP1KVLFzVu3FgjRoxQixYttHTp0kIPzws6/gg7zjjD+8sua/wRHtJOABAUOHwPAACgjGjevLm++eYbq8vwHXpKBQdfhYdZWdKWLY7rtBMABAV6SgEAACA0mOMI7dghuXkqarcRSnmPGR6a43R5yz//SLm5Uny8lJLi3WUDAHyCUAoAAAChoXJlKSnJcd0MkbwhJ+dUrx4OCyu9Jk0cl3//7d3l5g0ObTbvLhsA4BOEUgAAAAgdZuCxbp33lrl1q2S3O866V7u295ZbVp15puNyyxbHWfi8hXG/ACDoEEoBAAAgdJiBhzd74Zg9cBo1ksLYfS61KlWkChUkwzgVJHkDh1gCQNDhWxUAAAChwwylvNlTirDDu2w237QTPaUAIOgQSgEAACB0+DLsIJTyHl/2aKOdACBoEEoBAAAgdJhjSm3YIGVne2eZZthBDxzv8XZ4ePCgtHev47p5FkYAQMAjlAIAAEDoqFNHio11DEy+ZYt3lvnnn45LM0hB6Xk7lDLbqHZtKSHBO8sEAPgcoRQAAABCR1jYqcO3vBF47Nnj+JOks84q/fLgkLdHW05O6Zf3xx+Oy2bNSr8sAIDfEEoBAAAgtJiBhzdCKbMHTv36Ulxc6ZcHh7p1pehoKStL2rq19MsjlAKAoEQoBQAAgNDizUPDCDt8Izzcuz3aaCcACEqEUgAAAAgtZjDx+++lXxZhh+80beq4NLdxSRkG7QQAQYpQCgAAAKHl7LMdl3/+Wfoz8JlhR/PmpVsOCmrZ0nG5Zk3plpOeLu3f7xhPzDx0EwAQFAilAAAAEFrq1ZPi4x3jFa1fX/Ll0APHt8zwsLShlNlGDRs6zrwIAAgahFIAAAAILWFh3gk8/v1XysiQIiKkM87wSmnIw+wptWGDdOxYyZdDcAgAQYtQCgAAAKHHDKV++63ky1i71nHZuLEUFVX6muAqJUWqUsW1R1pJmG1MKAUAQYdQCgAAAKHH7IVTmlBq9WrH5TnnlLocFIF2AoAyjVAKAAAAoccbPaXMsKN169LXg8KVdrDz48elv/5yXKedACDoEEoBAAAg9DRr5hhbKj1dSksr2TJ+/tlxSdjhO6UND3/7TcrJcRwGWKOG9+oCAPgFoRQAAABCT7lyjrGgpFM9njyRlibt2iXZbKd688D78vaUys72/PFm2557rqOtAABBhVAKAAAAoalNG8fljz96/lgz7DjzTCk+3ns1wVWTJlJiopSZWbLBzjnEEgCCGqEUAAAAQpM3QinCDt8KC5MuuMBxnXYCgDKHUAoAAAChyQylVq50jDvkCTMgOfdc79aEgsx2WrHCs8dlZJzqXXXeed6tCQDgF4RSAAAACE1nnSXFxUlHjkjr1rn/uJwc6YcfHNc7dPBNbTilpD3afvxRys2V6tWTqlf3fl0AAJ8jlAIAAEBoCg8/1YPGk8Djjz+kw4cdY0m1aOGb2nCKefjehg3S/v3uP+677xyXBIcAELQIpQAAABC6zF4433/v/mPMsKNdOykiwvs1wVVSktSokeO6J4fwEUoBQNAjlAIAAEDouugix+XXX0uG4d5jCDv8r3Nnx+U337g3v91+qvcb7QQAQYtQCgAAAKGrQwcpKkrasUPauPH08+fmSkuWnHos/KNrV8flV1+5N//KldLx445eVk2a+K4uAIBPEUoBAAAgdJUr5zgMT3Iv8PjtNyk93TFAuvk4+N7FFzsuf/9dSks7/fyLFjkuu3eXwviXBgCCFZ/gAAAACG2e9MIxw46LL5aio31XE1xVriy1auW47s4hfGY7XXKJ72oCAPgcoRQABIg+fVz/AABe0q2b4zI1VTpxovh5CTusY7bTp58WP9+ePdLq1Y7r3bv7tiYAgE8RSgEAACC0nXuuVLOmdPSotHhx0fOlp58a5LxnT//UhlOuuMJxuXBh8eHhRx85Ls85R0pJ8XlZAADfIZQCAABAaAsLk/r1c1yfP7/o+ebPdwx0ft55Ur16/qkNp1xwgVSrliM8/PLLoud7913H5cCB/qkLAOAzhFIAAAAIff37Oy4//lg6dqzwed55x3E5aJB/aoIrm+1UO82dW/g8u3ZJ337ruD5ggF/KAgD4DqEUAAS5/GNRMR4VABSiXTupYUMpI0N6++2C969dK33/vRQeTg8cK117rePygw+k3bsL3v/SS5JhSO3bS3Xr+rU0AID3EUoBAACUQVlZWWrZsqVsNpvWrFljdTm+FxYm3Xyz4/r06Y7D9PJ69lnH5ZVXSjVq+Lc2nNKypSNwys6WXnjB9b4TJ6RZsxzXb7nF76UBALyPUAoAAKAMuvPOO1W9enWry/Cv4cOlxETpzz+lN988Nf2vv6TXX3dcHzfOmtpwytixjstnnnHtLTVtmmMw+tq1HeEhACDoEUoBAACUMV988YUWL16sJ5980upS/KtCBeneex3Xb7tN2rzZMb7UtddKOTlS375S27ZWVgjJMSh9mzaOthk+XLLbpV9+kSZPdtz/6KNSZKS1NQIAvCLC6gLgG4WNKbNwof/rAAB/yv/Zx+ceUFB6erpuuOEGffTRRypXrpxbj8nKylJWVpbzdkZGhiTJbrfLbrd7vUZzmb5Ytm66SeHz5ils9WoZrVtLiYmy7dgho1IlZT/5pCMAwWn5tI0k6bnnFNGpk2xffimjSRMpPV22EyeUe8klyunfn3Zyk8/bCV5BOwU+2shz7m4rQikAAIAywjAMDRs2TDfeeKPOPfdcbd261a3HTZkyRZPNXip5LF682O1gqyRSU1N9styYUaN0wcMPq8I//0iHD+tE+fL66c47dfCPP6Q//vDJOkOVr9pIkqrcdpvOffppRf7zjyRpb7NmWnXNNbIvWuSzdYYqX7YTvId2Cny0kfsyMzPdmo9QCgAAIMhNmDBBU6dOLXaedevWafHixTpy5IgmTpzo0fInTpyo8ePHO29nZGSoVq1a6t69uxITE0tUc3HsdrtSU1PVrVs3RfrqMK2BA5X97bfSsWMK79JFbRMSfLOeEOWXNurVSxo1StlLlkhVqqhChw7qFsboI57wSzuh1GinwEcbec7sVX06hFIAAABB7rbbbtOwYcOKnad+/fr65ptvtGLFCkVHR7vcd+6552rIkCF63RzsO5/o6OgCj5GkyMhIn+6c+3T5kZGO0AOl4uvXgFJSpKuv9t3yywiftxO8gnYKfLSR+9zdToRSgAcCYbyaPn0c+9FDh0oDBzqGVGDcnNBU2NhwCCx528h8XwJWSE5OVnJy8mnnmz59uh5++GHn7V27dqlHjx6aN2+eLrjggv9v796jmrzvP4C/AxJAAWEglyiEglcElcpkFJ3TorZeVnaxHMuU2c5uCtOKrjptB7VesDpnz2ZREXWzU+y89Kj1UkVBURREOBWxDLyBTmSKU4QqSL6/P3rMzxTQJE2eJyHv1zk5xzx5nu/zzvcbwtcPT74xZ0QiIiKiVliUIiIiIrIRAQEBOvddXFwAAMHBwejRo4cckYiIiMiG8UPZREREREREREQkOV4pRURERGSjAgMDIYSQOwYRERHZKBalJKDvujBtrQtkCWsY6aOt58isRJZFn/eTJ/s8vW7Zrl3GtaVPBkOO1actqTO05clab6Zg7vcmQ14Tz9tPapaai4iIiIj0x4/vERERERERERGR5FiUIiIiIiIiIiIiybEoRUREREREREREkuOaUqRD3zU6jF3Lpb1zPr1+TXOzfuuCcD2R/2fK9X3Idug7/uZ+nRi7rpExbX+f/azp/cXY98fv01+Gtv/d931D2yIiIiIi68crpYiIiIiIiIiISHIsShERERERERERkeQ6TFFqzZo1CAwMhJOTEyIjI1FQUCB3JCIiIiIiIiIiakeHWFNq+/btSE5Oxtq1axEZGYnVq1djzJgxKC8vh7e3t9zx9Cb1ui2WzNg1kvRpS999jD2nHOtyEX2X1K8vU68zZ4nkyGXKta4sYW0wOdoiIiIiIsvVIa6UWrVqFaZNm4apU6ciJCQEa9euRefOnbFx40a5oxERERERERERURusvijV1NSEoqIixMTEaLfZ2dkhJiYG+fn5MiYjIiIiIiIiIqL2WP3H927fvo2Wlhb4+PjobPfx8cHXX3/d5jGPHj3Co0ePtPfv3bsHAKirq0Pzd7+X2kjNzc1obGzEnTt3ADiYpE0AuHPHZE2Z/ZyGHfdtfwFt95e+bZmyf/RpS45c3zJNf9mWZ/cZfRf7y3Dy9Jml/rw/P5f+/SXfe+3/q6+vBwAIIcx3EivypB/u379vlvafzKPu378PBwe+B1kijpF14DhZB46T5eMYGe7JHOF5cyeFsPLZ1X/+8x90794dp06dQlRUlHb7u+++i9zcXJw5c6bVMampqfjggw+kjElEREQdQHV1NXr06CF3DNldv34d/v7+cscgIiIiC/e8uZPVXynl5eUFe3t73Lp1S2f7rVu34Ovr2+Yxf/zjH5GcnKy9r9FoUFdXB09PTygUCpPkun//Pvz9/VFdXQ03NzeTtNmRsb8Mw/4yHPvMMOwvw7HPDGNt/SWEQH19PVQqldxRLIJKpUJ1dTVcXV1NNnd6mrW9PmwRx8g6cJysA8fJ8nGMDKfv3Mnqi1JKpRKDBw9GdnY2YmNjAXxbZMrOzkZSUlKbxzg6OsLR0VFnm7u7u1nyubm58UVrAPaXYdhfhmOfGYb9ZTj2mWGsqb+6du0qdwSLYWdnJ8kVY9b0+rBVHCPrwHGyDhwny8cxMow+cyerL0oBQHJyMhISEhAREYEhQ4Zg9erVaGhowNSpU+WORkREREREREREbegQRam4uDj897//xZ/+9CfU1NRg0KBBOHjwYKvFz4mIiIiIiIiIyDJ0iKIUACQlJbX7cT05ODo6IiUlpdXHBKlt7C/DsL8Mxz4zDPvLcOwzw7C/6Fn4+rB8HCPrwHGyDhwny8cxMh+r//Y9IiIiIiIiIiKyPnZyByAiIiIiIiIiItvDohQREREREREREUmORSkiIiIiIiIiIpIci1JmsGbNGgQGBsLJyQmRkZEoKCiQO5LFOn78OCZMmACVSgWFQoHPP/9c7kgWbdmyZfjhD38IV1dXeHt7IzY2FuXl5XLHsljp6ekYMGAA3Nzc4ObmhqioKBw4cEDuWFYlLS0NCoUC77zzjtxRLFJqaioUCoXOrW/fvnLHsng3btzAr371K3h6esLZ2RlhYWE4e/as3LFIYobOl/71r3+hb9++cHJyQlhYGPbv3y9RUttlyBhlZGRg2LBh8PDwgIeHB2JiYjgHloix//fIysqCQqFAbGyseQMSAMPH6X//+x8SExPh5+cHR0dH9O7dm+97ZmboGK1evRp9+vSBs7Mz/P39MXv2bDx8+FCitB0Hi1Imtn37diQnJyMlJQXnzp3DwIEDMWbMGNTW1sodzSI1NDRg4MCBWLNmjdxRrEJubi4SExNx+vRpHD58GM3NzRg9ejQaGhrkjmaRevTogbS0NBQVFeHs2bMYOXIkXnvtNVy4cEHuaFahsLAQ69atw4ABA+SOYtH69++Pmzdvam95eXlyR7Jod+/eRXR0NBwcHHDgwAGUlZXhz3/+Mzw8POSORhIydL506tQpTJo0CW+99RaKi4sRGxuL2NhYlJaWSpzcdhg6Rjk5OZg0aRKOHTuG/Px8+Pv7Y/To0bhx44bEyW2Lsf/3uHr1KubOnYthw4ZJlNS2GTpOTU1NGDVqFK5evYodO3agvLwcGRkZ6N69u8TJbYehY7R161bMnz8fKSkpuHjxIjIzM7F9+3YsWLBA4uQdgCCTGjJkiEhMTNTeb2lpESqVSixbtkzGVNYBgNi9e7fcMaxKbW2tACByc3PljmI1PDw8xIYNG+SOYfHq6+tFr169xOHDh8Xw4cPFrFmz5I5kkVJSUsTAgQPljmFV5s2bJ4YOHSp3DJKZofOl119/XYwbN05nW2RkpPjtb39r1py27PvOaR8/fixcXV3F3//+d3NFJGHcOD1+/Fi89NJLYsOGDSIhIUG89tprEiS1bYaOU3p6uggKChJNTU1SRbR5ho5RYmKiGDlypM625ORkER0dbdacHRGvlDKhpqYmFBUVISYmRrvNzs4OMTExyM/PlzEZdVT37t0DAPzgBz+QOYnla2lpQVZWFhoaGhAVFSV3HIuXmJiIcePG6byfUdsqKiqgUqkQFBSE+Ph4VFVVyR3Jou3ZswcRERGYOHEivL29ER4ejoyMDLljkYSMmS/l5+e3ej8aM2YM51dmYoo5bWNjI5qbmzlHMSNjx2nRokXw9vbGW2+9JUVMm2fMOO3ZswdRUVFITEyEj48PQkNDsXTpUrS0tEgV26YYM0YvvfQSioqKtB/xu3z5Mvbv34+xY8dKkrkj6SR3gI7k9u3baGlpgY+Pj852Hx8ffP311zKloo5Ko9HgnXfeQXR0NEJDQ+WOY7HOnz+PqKgoPHz4EC4uLti9ezdCQkLkjmXRsrKycO7cORQWFsodxeJFRkZi8+bN6NOnD27evIkPPvgAw4YNQ2lpKVxdXeWOZ5EuX76M9PR0JCcnY8GCBSgsLMTMmTOhVCqRkJAgdzySgDHzpZqamjb3r6mpMVtOW2aKOe28efOgUqn4xw0zMmac8vLykJmZiZKSEgkSEmDcOF2+fBlHjx5FfHw89u/fj8rKSsyYMQPNzc1ISUmRIrZNMWaM3njjDdy+fRtDhw6FEAKPHz/G7373O358zwgsShFZqcTERJSWlnL9mufo06cPSkpKcO/ePezYsQMJCQnIzc1lYaod1dXVmDVrFg4fPgwnJye541i8V199VfvvAQMGIDIyEmq1Gp999hn/At0OjUaDiIgILF26FAAQHh6O0tJSrF27lkUpog4iLS0NWVlZyMnJ4e8SC1JfX4/JkycjIyMDXl5ecsehZ9BoNPD29sb69ethb2+PwYMH48aNG1ixYgWLUhYiJycHS5cuxSeffILIyEhUVlZi1qxZ+PDDD/H+++/LHc+qsChlQl5eXrC3t8etW7d0tt+6dQu+vr4ypaKOKCkpCfv27cPx48fRo0cPueNYNKVSiZ49ewIABg8ejMLCQnz88cdYt26dzMksU1FREWpra/Hiiy9qt7W0tOD48eP429/+hkePHsHe3l7GhJbN3d0dvXv3RmVlpdxRLJafn1+ronC/fv2wc+dOmRKR1IyZL/n6+nJ+JaHvM6dduXIl0tLScOTIEX5RhpkZOk6XLl3C1atXMWHCBO02jUYDAOjUqRPKy8sRHBxs3tA2yJifJz8/Pzg4OOjMufr164eamho0NTVBqVSaNbOtMWaM3n//fUyePBm/+c1vAABhYWFoaGjA22+/jYULF8LOjisl6Ys9ZUJKpRKDBw9Gdna2dptGo0F2djbXsCGTEEIgKSkJu3fvxtGjR/HCCy/IHcnqaDQaPHr0SO4YFuvll1/G+fPnUVJSor1FREQgPj4eJSUlLEg9x4MHD3Dp0iX4+fnJHcViRUdHo7y8XGfbv//9b6jVapkSkdSMmS9FRUXp7A8Ahw8f5vzKTIyd03700Uf48MMPcfDgQUREREgR1aYZOk59+/Zt9Tv+pz/9KUaMGIGSkhL4+/tLGd9mGPPzFB0djcrKSm3REPj2d6Wfnx8LUmZgzBg1Nja2Kjw9mScLIcwXtiOSeaH1DicrK0s4OjqKzZs3i7KyMvH2228Ld3d3UVNTI3c0i1RfXy+Ki4tFcXGxACBWrVoliouLxbVr1+SOZpGmT58uunbtKnJycsTNmze1t8bGRrmjWaT58+eL3NxcceXKFfHVV1+J+fPnC4VCIb788ku5o1kVfvte++bMmSNycnLElStXxMmTJ0VMTIzw8vIStbW1ckezWAUFBaJTp05iyZIloqKiQvzzn/8UnTt3Fp9++qnc0UhCz5svTZ48WcyfP1+7/8mTJ0WnTp3EypUrxcWLF0VKSopwcHAQ58+fl+spdHiGjlFaWppQKpVix44dOnOU+vp6uZ6CTTB0nL6L374nDUPHqaqqSri6uoqkpCRRXl4u9u3bJ7y9vcXixYvlegodnqFjlJKSIlxdXcW2bdvE5cuXxZdffimCg4PF66+/LtdTsFosSpnBX//6VxEQECCUSqUYMmSIOH36tNyRLNaxY8cEgFa3hIQEuaNZpLb6CoDYtGmT3NEs0ptvvinUarVQKpWiW7du4uWXX2ZByggsSrUvLi5O+Pn5CaVSKbp37y7i4uJEZWWl3LEs3t69e0VoaKhwdHQUffv2FevXr5c7EsngWfOl4cOHt5oLfPbZZ6J3795CqVSK/v37iy+++ELixLbHkDFSq9VtzlFSUlKkD25jDP1ZehqLUtIxdJxOnTolIiMjhaOjowgKChJLliwRjx8/lji1bTFkjJqbm0VqaqoIDg4WTk5Owt/fX8yYMUPcvXtX+uBWTiEEry0jIiIiIiIiIiJpcU0pIiIiIiIiIiKSHItSREREREREREQkORaliIiIiIiIiIhIcixKERERERERERGR5FiUIiIiIiIiIiIiybEoRUREREREREREkmNRioiIiIiIiIiIJMeiFBERERERERERSY5FKSIiIiIiIiIikhyLUkRksTZv3gx3d3e5Y7QpOzsb/fr1Q0tLi8nbvnr1KhQKBUpKSgAAZWVl6NGjBxoaGkx+LiIiIiJjmGIu1NTUhMDAQJw9e9aEyYjImrAoRUSy+fWvfw2FQgGFQgGlUomePXti0aJFePz4sdzRnuvdd9/Fe++9B3t7e7OfKyQkBD/60Y+watUqs5+LiIiISB+mmAsplUrMnTsX8+bNM2EyIrImLEoRkaxeeeUV3Lx5ExUVFZgzZw5SU1OxYsUKuWM9U15eHi5duoRf/OIX7e7T1NRk0nNOnToV6enpVlGwIyIioo5Nn7mQvuLj45GXl4cLFy6YIBkRWRsWpYhIVo6OjvD19YVarcb06dMRExODPXv26Oxz6NAh9OvXDy4uLtoi1hOFhYUYNWoUvLy80LVrVwwfPhznzp3TPi6EQGpqKgICAuDo6AiVSoWZM2dqH3/06BHmzp2L7t27o0uXLoiMjEROTs4zM2dlZWHUqFFwcnLSbktNTcWgQYOwYcMGvPDCC9rHDh48iKFDh8Ld3R2enp4YP348Ll26pNNeQUEBwsPD4eTkhIiICBQXF7c656hRo1BXV4fc3NzndyoRERGRnp4sG/Dd209+8pN2j3nWXGjjxo0ICAiAi4sLZsyYgZaWFnz00Ufw9fWFt7c3lixZotOWh4cHoqOjkZWVZa6nSEQWjEUpIrIozs7OOlcZNTY2YuXKldiyZQuOHz+OqqoqzJ07V/t4fX09EhISkJeXh9OnT6NXr14YO3Ys6uvrAQA7d+7EX/7yF6xbtw4VFRX4/PPPERYWpj0+KSkJ+fn5yMrKwldffYWJEyfilVdeQUVFRbsZT5w4gYiIiFbbKysrsXPnTuzatUu7HlRDQwOSk5Nx9uxZZGdnw87ODj/72c+g0WgAAA8ePMD48eMREhKCoqIipKam6jy/J5RKJQYNGoQTJ04Y1qFEREREz+Dv74+bN29qb8XFxfD09MSPf/zjdo9pby506dIlHDhwAAcPHsS2bduQmZmJcePG4fr168jNzcXy5cvx3nvv4cyZMzrHDRkyhHMcIhvVSe4ARETAt1c0ZWdn49ChQ/j973+v3d7c3Iy1a9ciODgYwLdFpEWLFmkfHzlypE4769evh7u7O3JzczF+/HhUVVXB19cXMTExcHBwQEBAAIYMGQIAqKqqwqZNm1BVVQWVSgUAmDt3Lg4ePIhNmzZh6dKlbWa9du2adv+nNTU14R//+Ae6deum3fbdy9o3btyIbt26oaysDKGhodi6dSs0Gg0yMzPh5OSE/v374/r165g+fXqr9lUqFa5du/bMfiQiIiIyhL29PXx9fQEADx8+RGxsLKKiopCamtruMe3NhTQaDTZu3AhXV1eEhIRgxIgRKC8vx/79+2FnZ4c+ffpg+fLlOHbsGCIjI7XHcY5DZLt4pRQRyWrfvn1wcXGBk5MTXn31VcTFxelMgjp37qwtSAGAn58famtrtfdv3bqFadOmoVevXujatSvc3Nzw4MEDVFVVAQAmTpyIb775BkFBQZg2bRp2796tXZfp/PnzaGlpQe/eveHi4qK95ebmtvqI3dO++eYbncvVn1Cr1ToFKQCoqKjApEmTEBQUBDc3NwQGBgKANt/FixcxYMAAnfaioqLaPK+zszMaGxvbzUVERET0fbz55puor6/H1q1bYWfX/n8V25sLBQYGwtXVVXvfx8cHISEhOm35+PjozOUAznGIbBmvlCIiWY0YMQLp6elQKpVQqVTo1En3bcnBwUHnvkKhgBBCez8hIQF37tzBxx9/DLVaDUdHR0RFRWk/Aujv74/y8nIcOXIEhw8fxowZM7BixQrk5ubiwYMHsLe3R1FRUatvjnFxcWk3s5eXF+7evdtqe5cuXVptmzBhAtRqNTIyMqBSqaDRaBAaGmrUQuh1dXU6BToiIiIiU1m8eDEOHTqEgoICncJSW9qbC7U1b2tr25NlDJ6oq6tr9Yc9IrINLEoRkay6dOmCnj17Gn38yZMn8cknn2Ds2LEAgOrqaty+fVtnH2dnZ0yYMAETJkxAYmIi+vbti/PnzyM8PBwtLS2ora3FsGHD9D5neHg4ysrKnrvfnTt3UF5ejoyMDG37eXl5Ovv069cPW7ZswcOHD7V/cTx9+nSb7ZWWluKXv/yl3jmJiIiI9LFz504sWrQIBw4c0OsPYPrOhfRVWlqK8PBwk7VHRNaDH98jIqvWq1cvbNmyBRcvXsSZM2cQHx8PZ2dn7eObN29GZmYmSktLcfnyZXz66adwdnaGWq1G7969ER8fjylTpmDXrl24cuUKCgoKsGzZMnzxxRftnnPMmDGtiktt8fDwgKenJ9avX4/KykocPXoUycnJOvu88cYbUCgUmDZtGsrKyrB//36sXLmyVVtXr17FjRs3EBMTY0DvEBERET1baWkppkyZgnnz5qF///6oqalBTU0N6urq2j1G37mQvk6cOIHRo0ebrD0ish4sShGRVcvMzMTdu3fx4osvYvLkyZg5cya8vb21j7u7uyMjIwPR0dEYMGAAjhw5gr1798LT0xMAsGnTJkyZMgVz5sxBnz59EBsbi8LCQgQEBLR7zvj4eFy4cAHl5eXPzGZnZ4esrCwUFRUhNDQUs2fPxooVK3T2cXFxwd69e7VXbi1cuBDLly9v1da2bdswevRoqNVqQ7qHiIiI6JnOnj2LxsZGLF68GH5+ftrbz3/+83aP0XcupI/8/Hzcu3ePV4MT2SiFeHpxFiIi0ssf/vAH3L9/H+vWrTP7uZqamtCrVy9s3boV0dHRZj8fERER0fOYai4UFxeHgQMHYsGCBSZKRkTWhFdKEREZYeHChVCr1a0W6jSHqqoqLFiwgAUpIiIishimmAs1NTUhLCwMs2fPNmEyIrImvFKKiIiIiIiIiIgkxyuliIiIiIiIiIhIcixKERERERERERGR5FiUIiIiIiIiIiIiybEoRUREREREREREkmNRioiIiIiIiIiIJMeiFBERERERERERSY5FKSIiIiIiIiIikhyLUkREREREREREJDkWpYiIiIiIiIiISHL/B7w6VxTWNUGgAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Constants\n", "U0 = 511e3 # Rest energy of the electron in eV (mc^2/e)\n", "c = 3e8 # Speed of light in vacuum (m/s)\n", "omega = 2 * np.pi * 1e9 # Angular frequency (for example, 1 GHz)\n", "f = 1.5 * 1e9 # Frequency\n", "phi_0 = 0 # Initial phase\n", "E0 = -40e6 # Electric field strength in V/m (example value)\n", "dz = 1e-5 # Step size in m\n", "z_max = 0.9 # Length of the buncher in m\n", "z_max_grouper = 0.3 # Length of the buncher in m\n", "num_particles = 1_000 # Number of particles\n", "\n", "# Initial conditions\n", "betas = np.full(num_particles, 0.7) # Initial beta for all particles\n", "phis = np.linspace(0, np.pi, num_particles) # Uniform distribution of initial phases\n", "\n", "# Function to calculate derivatives\n", "def derivatives(beta, phi, E):\n", " dbeta_dz = (E / U0) * np.cos(phi + phi_0) * ((1 - beta**2)**(3/2)) / beta\n", " dphi_dz = omega / (beta * c)\n", " return dbeta_dz, dphi_dz\n", "\n", "# Function to calculate Ez(z)\n", "def E_z(z):\n", " return np.where(z < z_max_grouper, E0 * np.sin(2 * np.pi * f * z / c + phi_0), 0)\n", "\n", "# Solving the system using Euler's method\n", "z_values = np.arange(0, z_max, dz)\n", "betas_values = []\n", "phis_values = []\n", "\n", "for z in z_values:\n", " dbeta_dz, dphi_dz = derivatives(betas, phis, E_z(z))\n", " betas += dbeta_dz * dz\n", " phis += dphi_dz * dz\n", " betas_values.append(betas.copy())\n", " phis_values.append(phis.copy())\n", "\n", "# Correcting phase to be within [0, 2*pi]\n", "phis = phis % (2 * np.pi)\n", "\n", "# Plotting the histogram of particle phases at the output\n", "plt.figure(figsize=(12, 5))\n", "plt.subplot(1, 2, 1)\n", "plt.hist(phis, bins=100, color='blue', alpha=0.7)\n", "plt.xlabel('Phase (rad)')\n", "plt.ylabel('Number of Particles')\n", "plt.title('Particle Phase Distribution at Microwave Buncher Output')\n", "plt.grid(True)\n", "\n", "# Plotting Ez(z)\n", "Ez_values = E_z(z_values)\n", "plt.subplot(1, 2, 2)\n", "plt.plot(z_values, Ez_values, label='$E_z(z)$', color='red')\n", "plt.xlabel('z (m)')\n", "plt.ylabel('$E_z$ (V/m)')\n", "plt.title('Electric Field Strength Along the Buncher')\n", "plt.grid(True)\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.4" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 4 }