Exploring SPS.ipynb

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      "Defaulting to user installation because normal site-packages is not writeable\n",
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    "pip install xsuite"
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     "text": [
      "Done loading line from dict.           \n",
      "Compiling ContextCpu kernels...\n",
      "Done compiling ContextCpu kernels.\n"
     ]
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   "source": [
    "%matplotlib widget\n",
    "import ipympl\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import xpart as xp\n",
    "import xtrack as xt\n",
    "\n",
    "fname_model = './generate_models/sps_acceleration.json'\n",
    "\n",
    "nemitt_x = 2.5e-6\n",
    "nemitt_y = 2.5e-6\n",
    "\n",
    "line = xt.Line.from_json(fname_model)\n",
    "line.build_tracker()"
   ]
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   "source": [
    "## Exploring the SPS\n",
    "\n",
    "The beamline of the SPS is accessible through `line`. Some examples on how we can access the elements of the line.\n",
    "\n",
    "### Enumerate elements and their names"
   ]
  },
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   "execution_count": 3,
   "id": "3757f3de",
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       " 'mbb.53150_dex',\n",
       " 'drift_187',\n",
       " 'mba.53170_den',\n",
       " 'drift_188',\n",
       " 'mba.53170_aper',\n",
       " 'mba.53170',\n",
       " 'drift_189',\n",
       " 'mba.53170_dex',\n",
       " 'drift_190',\n",
       " 'mba.53190_den',\n",
       " 'drift_191',\n",
       " 'mba.53190_aper',\n",
       " 'mba.53190',\n",
       " 'drift_192',\n",
       " 'mba.53190_dex',\n",
       " 'drift_193',\n",
       " 'lsf.53205_aper',\n",
       " 'lsf.53205',\n",
       " 'drift_194',\n",
       " 'mdh.53207_aper',\n",
       " 'mdh.53207',\n",
       " 'drift_195',\n",
       " 'bph.53208_aper',\n",
       " 'bph.53208',\n",
       " 'drift_196',\n",
       " 'qf.53210_aper',\n",
       " 'qf.53210',\n",
       " 'drift_197',\n",
       " 'mba.53230_den',\n",
       " 'drift_198',\n",
       " 'mba.53230_aper',\n",
       " 'mba.53230',\n",
       " 'drift_199',\n",
       " 'mba.53230_dex',\n",
       " 'drift_200',\n",
       " 'mba.53250_den',\n",
       " 'drift_201',\n",
       " 'mba.53250_aper',\n",
       " 'mba.53250',\n",
       " 'drift_202',\n",
       " 'mba.53250_dex',\n",
       " 'drift_203',\n",
       " 'mbb.53270_den',\n",
       " 'drift_204',\n",
       " 'mbb.53270_aper',\n",
       " 'mbb.53270',\n",
       " 'drift_205',\n",
       " 'mbb.53270_dex',\n",
       " 'drift_206',\n",
       " 'mbb.53290_den',\n",
       " 'drift_207',\n",
       " 'mbb.53290_aper',\n",
       " 'mbb.53290',\n",
       " 'drift_208',\n",
       " 'mbb.53290_dex',\n",
       " 'drift_209',\n",
       " 'lod.53302_aper',\n",
       " 'lod.53302',\n",
       " 'drift_210',\n",
       " 'mdv.53307_aper',\n",
       " 'mdv.53307',\n",
       " 'drift_211',\n",
       " 'bpv.53308_aper',\n",
       " 'bpv.53308',\n",
       " 'drift_212',\n",
       " 'qd.53310_aper',\n",
       " 'qd.53310',\n",
       " 'drift_213',\n",
       " 'mbb.53330_den',\n",
       " 'drift_214',\n",
       " 'mbb.53330_aper',\n",
       " 'mbb.53330',\n",
       " 'drift_215',\n",
       " 'mbb.53330_dex',\n",
       " 'drift_216',\n",
       " 'mbb.53350_den',\n",
       " 'drift_217',\n",
       " 'mbb.53350_aper',\n",
       " 'mbb.53350',\n",
       " 'drift_218',\n",
       " 'mbb.53350_dex',\n",
       " 'drift_219',\n",
       " 'mba.53370_den',\n",
       " 'drift_220',\n",
       " 'mba.53370_aper',\n",
       " 'mba.53370',\n",
       " 'drift_221',\n",
       " 'mba.53370_dex',\n",
       " 'drift_222',\n",
       " 'mba.53390_den',\n",
       " 'drift_223',\n",
       " 'mba.53390_aper',\n",
       " 'mba.53390',\n",
       " 'drift_224',\n",
       " 'mba.53390_dex',\n",
       " 'drift_225',\n",
       " 'qecd.53402',\n",
       " 'drift_226',\n",
       " 'mdh.53407_aper',\n",
       " 'mdh.53407',\n",
       " 'drift_227',\n",
       " 'bph.53408_aper',\n",
       " 'bph.53408',\n",
       " 'drift_228',\n",
       " 'qf.53410_aper',\n",
       " 'qf.53410',\n",
       " 'drift_229',\n",
       " 'mba.53430_den',\n",
       " 'drift_230',\n",
       " 'mba.53430_aper',\n",
       " 'mba.53430',\n",
       " 'drift_231',\n",
       " 'mba.53430_dex',\n",
       " 'drift_232',\n",
       " 'mba.53450_den',\n",
       " 'drift_233',\n",
       " 'mba.53450_aper',\n",
       " 'mba.53450',\n",
       " 'drift_234',\n",
       " 'mba.53450_dex',\n",
       " 'drift_235',\n",
       " 'mbb.53470_den',\n",
       " 'drift_236',\n",
       " 'mbb.53470_aper',\n",
       " 'mbb.53470',\n",
       " 'drift_237',\n",
       " 'mbb.53470_dex',\n",
       " 'drift_238',\n",
       " 'mbb.53490_den',\n",
       " 'drift_239',\n",
       " 'mbb.53490_aper',\n",
       " 'mbb.53490',\n",
       " 'drift_240',\n",
       " 'mbb.53490_dex',\n",
       " 'drift_241',\n",
       " 'lod.53502_aper',\n",
       " 'lod.53502',\n",
       " 'drift_242',\n",
       " 'lsd.53505_aper',\n",
       " 'lsd.53505',\n",
       " 'drift_243',\n",
       " 'mdv.53507_aper',\n",
       " 'mdv.53507',\n",
       " 'drift_244',\n",
       " 'bpv.53508_aper',\n",
       " 'bpv.53508',\n",
       " 'drift_245',\n",
       " 'qd.53510_aper',\n",
       " 'qd.53510',\n",
       " 'drift_246',\n",
       " 'mbb.53530_den',\n",
       " 'drift_247',\n",
       " 'mbb.53530_aper',\n",
       " 'mbb.53530',\n",
       " 'drift_248',\n",
       " 'mbb.53530_dex',\n",
       " 'drift_249',\n",
       " 'mbb.53550_den',\n",
       " 'drift_250',\n",
       " 'mbb.53550_aper',\n",
       " 'mbb.53550',\n",
       " 'drift_251',\n",
       " 'mbb.53550_dex',\n",
       " 'drift_252',\n",
       " 'mba.53570_den',\n",
       " 'drift_253',\n",
       " 'mba.53570_aper',\n",
       " 'mba.53570',\n",
       " 'drift_254',\n",
       " 'mba.53570_dex',\n",
       " 'drift_255',\n",
       " 'mba.53590_den',\n",
       " 'drift_256',\n",
       " 'mba.53590_aper',\n",
       " 'mba.53590',\n",
       " 'drift_257',\n",
       " 'mba.53590_dex',\n",
       " 'drift_258',\n",
       " 'loen.53602_aper',\n",
       " 'loen.53602',\n",
       " 'drift_259',\n",
       " 'lsf.53605_aper',\n",
       " 'lsf.53605',\n",
       " 'drift_260',\n",
       " 'mdh.53607_aper',\n",
       " 'mdh.53607',\n",
       " 'drift_261',\n",
       " 'bph.53608_aper',\n",
       " 'bph.53608',\n",
       " 'drift_262',\n",
       " 'qf.60010_aper',\n",
       " 'qf.60010',\n",
       " 'drift_263',\n",
       " 'mba.60030_den',\n",
       " 'drift_264',\n",
       " 'mba.60030_aper',\n",
       " 'mba.60030',\n",
       " 'drift_265',\n",
       " 'mba.60030_dex',\n",
       " 'drift_266',\n",
       " 'mba.60050_den',\n",
       " 'drift_267',\n",
       " 'mba.60050_aper',\n",
       " 'mba.60050',\n",
       " 'drift_268',\n",
       " 'mba.60050_dex',\n",
       " 'drift_269',\n",
       " 'mbb.60070_den',\n",
       " 'drift_270',\n",
       " 'mbb.60070_aper',\n",
       " 'mbb.60070',\n",
       " 'drift_271',\n",
       " 'mbb.60070_dex',\n",
       " 'drift_272',\n",
       " 'mbb.60090_den',\n",
       " 'drift_273',\n",
       " 'mbb.60090_aper',\n",
       " 'mbb.60090',\n",
       " 'drift_274',\n",
       " 'mbb.60090_dex',\n",
       " 'drift_275',\n",
       " 'lsd.60105_aper',\n",
       " 'lsd.60105',\n",
       " 'drift_276',\n",
       " 'mdv.60107_aper',\n",
       " 'mdv.60107',\n",
       " 'drift_277',\n",
       " 'bpv.60108_aper',\n",
       " 'bpv.60108',\n",
       " 'drift_278',\n",
       " 'qd.60110_aper',\n",
       " 'qd.60110',\n",
       " 'drift_279',\n",
       " 'mbb.60130_den',\n",
       " 'drift_280',\n",
       " 'mbb.60130_aper',\n",
       " 'mbb.60130',\n",
       " 'drift_281',\n",
       " 'mbb.60130_dex',\n",
       " 'drift_282',\n",
       " 'mbb.60150_den',\n",
       " 'drift_283',\n",
       " 'mbb.60150_aper',\n",
       " 'mbb.60150',\n",
       " 'drift_284',\n",
       " 'mbb.60150_dex',\n",
       " 'drift_285',\n",
       " 'mba.60170_den',\n",
       " 'drift_286',\n",
       " 'mba.60170_aper',\n",
       " 'mba.60170',\n",
       " 'drift_287',\n",
       " 'mba.60170_dex',\n",
       " 'drift_288',\n",
       " 'mba.60190_den',\n",
       " 'drift_289',\n",
       " 'mba.60190_aper',\n",
       " 'mba.60190',\n",
       " 'drift_290',\n",
       " 'mba.60190_dex',\n",
       " 'drift_291',\n",
       " 'lsf.60205_aper',\n",
       " 'lsf.60205',\n",
       " 'drift_292',\n",
       " 'mdh.60207_aper',\n",
       " 'mdh.60207',\n",
       " 'drift_293',\n",
       " 'bph.60208_aper',\n",
       " 'bph.60208',\n",
       " 'drift_294',\n",
       " 'qf.60210_aper',\n",
       " 'qf.60210',\n",
       " 'drift_295',\n",
       " 'mba.60230_den',\n",
       " 'drift_296',\n",
       " 'mba.60230_aper',\n",
       " 'mba.60230',\n",
       " 'drift_297',\n",
       " 'mba.60230_dex',\n",
       " 'drift_298',\n",
       " 'mba.60250_den',\n",
       " 'drift_299',\n",
       " 'mba.60250_aper',\n",
       " 'mba.60250',\n",
       " 'drift_300',\n",
       " 'mba.60250_dex',\n",
       " 'drift_301',\n",
       " 'mbb.60270_den',\n",
       " 'drift_302',\n",
       " 'mbb.60270_aper',\n",
       " 'mbb.60270',\n",
       " 'drift_303',\n",
       " 'mbb.60270_dex',\n",
       " 'drift_304',\n",
       " 'mbb.60290_den',\n",
       " 'drift_305',\n",
       " 'mbb.60290_aper',\n",
       " 'mbb.60290',\n",
       " 'drift_306',\n",
       " 'mbb.60290_dex',\n",
       " 'drift_307',\n",
       " 'qe.60302',\n",
       " 'drift_308',\n",
       " 'lsd.60305_aper',\n",
       " 'lsd.60305',\n",
       " 'drift_309',\n",
       " 'mdv.60307_aper',\n",
       " 'mdv.60307',\n",
       " 'drift_310',\n",
       " 'bpv.60308_aper',\n",
       " 'bpv.60308',\n",
       " 'drift_311',\n",
       " 'qd.60310_aper',\n",
       " 'qd.60310',\n",
       " 'drift_312',\n",
       " 'mbb.60330_den',\n",
       " 'drift_313',\n",
       " 'mbb.60330_aper',\n",
       " 'mbb.60330',\n",
       " 'drift_314',\n",
       " 'mbb.60330_dex',\n",
       " 'drift_315',\n",
       " 'mbb.60350_den',\n",
       " 'drift_316',\n",
       " 'mbb.60350_aper',\n",
       " 'mbb.60350',\n",
       " 'drift_317',\n",
       " 'mbb.60350_dex',\n",
       " 'drift_318',\n",
       " 'mba.60370_den',\n",
       " 'drift_319',\n",
       " 'mba.60370_aper',\n",
       " 'mba.60370',\n",
       " 'drift_320',\n",
       " 'mba.60370_dex',\n",
       " 'drift_321',\n",
       " 'mba.60390_den',\n",
       " 'drift_322',\n",
       " 'mba.60390_aper',\n",
       " 'mba.60390',\n",
       " 'drift_323',\n",
       " 'mba.60390_dex',\n",
       " 'drift_324',\n",
       " 'qe.60402',\n",
       " 'drift_325',\n",
       " 'mdh.60407_aper',\n",
       " 'mdh.60407',\n",
       " 'drift_326',\n",
       " 'bph.60408_aper',\n",
       " 'bph.60408',\n",
       " 'drift_327',\n",
       " 'qf.60410_aper',\n",
       " 'qf.60410',\n",
       " 'drift_328',\n",
       " 'mba.60430_den',\n",
       " 'drift_329',\n",
       " 'mba.60430_aper',\n",
       " 'mba.60430',\n",
       " 'drift_330',\n",
       " 'mba.60430_dex',\n",
       " 'drift_331',\n",
       " 'mba.60450_den',\n",
       " 'drift_332',\n",
       " 'mba.60450_aper',\n",
       " 'mba.60450',\n",
       " 'drift_333',\n",
       " 'mba.60450_dex',\n",
       " 'drift_334',\n",
       " 'mbb.60470_den',\n",
       " 'drift_335',\n",
       " 'mbb.60470_aper',\n",
       " 'mbb.60470',\n",
       " 'drift_336',\n",
       " 'mbb.60470_dex',\n",
       " 'drift_337',\n",
       " 'mbb.60490_den',\n",
       " 'drift_338',\n",
       " 'mbb.60490_aper',\n",
       " 'mbb.60490',\n",
       " 'drift_339',\n",
       " 'mbb.60490_dex',\n",
       " 'drift_340',\n",
       " 'qe.60502',\n",
       " 'drift_341',\n",
       " 'mdv.60507_aper',\n",
       " 'mdv.60507',\n",
       " 'drift_342',\n",
       " 'bpv.60508_aper',\n",
       " 'bpv.60508',\n",
       " 'drift_343',\n",
       " 'qd.60510_aper',\n",
       " 'qd.60510',\n",
       " 'drift_344',\n",
       " 'mbb.60530_den',\n",
       " 'drift_345',\n",
       " 'mbb.60530_aper',\n",
       " 'mbb.60530',\n",
       " 'drift_346',\n",
       " 'mbb.60530_dex',\n",
       " 'drift_347',\n",
       " 'mbb.60550_den',\n",
       " 'drift_348',\n",
       " 'mbb.60550_aper',\n",
       " 'mbb.60550',\n",
       " 'drift_349',\n",
       " 'mbb.60550_dex',\n",
       " 'drift_350',\n",
       " 'mba.60570_den',\n",
       " 'drift_351',\n",
       " 'mba.60570_aper',\n",
       " 'mba.60570',\n",
       " 'drift_352',\n",
       " 'mba.60570_dex',\n",
       " 'drift_353',\n",
       " 'mba.60590_den',\n",
       " 'drift_354',\n",
       " 'mba.60590_aper',\n",
       " 'mba.60590',\n",
       " 'drift_355',\n",
       " 'mba.60590_dex',\n",
       " 'drift_356',\n",
       " 'qe.60602',\n",
       " 'drift_357',\n",
       " 'mdh.60607_aper',\n",
       " 'mdh.60607',\n",
       " 'drift_358',\n",
       " 'bph.60608_aper',\n",
       " 'bph.60608',\n",
       " 'drift_359',\n",
       " 'qf.60610_aper',\n",
       " 'qf.60610',\n",
       " 'drift_360',\n",
       " 'mba.60630_den',\n",
       " 'drift_361',\n",
       " 'mba.60630_aper',\n",
       " 'mba.60630',\n",
       " 'drift_362',\n",
       " 'mba.60630_dex',\n",
       " 'drift_363',\n",
       " 'mba.60650_den',\n",
       " 'drift_364',\n",
       " 'mba.60650_aper',\n",
       " 'mba.60650',\n",
       " 'drift_365',\n",
       " 'mba.60650_dex',\n",
       " 'drift_366',\n",
       " 'mbb.60670_den',\n",
       " 'drift_367',\n",
       " 'mbb.60670_aper',\n",
       " 'mbb.60670',\n",
       " 'drift_368',\n",
       " 'mbb.60670_dex',\n",
       " 'drift_369',\n",
       " 'mbb.60690_den',\n",
       " 'drift_370',\n",
       " 'mbb.60690_aper',\n",
       " 'mbb.60690',\n",
       " 'drift_371',\n",
       " 'mbb.60690_dex',\n",
       " 'drift_372',\n",
       " 'lod.60702_aper',\n",
       " 'lod.60702',\n",
       " 'drift_373',\n",
       " 'mdv.60707_aper',\n",
       " 'mdv.60707',\n",
       " 'drift_374',\n",
       " 'bpv.60708_aper',\n",
       " 'bpv.60708',\n",
       " 'drift_375',\n",
       " 'qd.60710_aper',\n",
       " 'qd.60710',\n",
       " 'drift_376',\n",
       " 'mbb.60730_den',\n",
       " 'drift_377',\n",
       " 'mbb.60730_aper',\n",
       " 'mbb.60730',\n",
       " 'drift_378',\n",
       " 'mbb.60730_dex',\n",
       " 'drift_379',\n",
       " 'mbb.60750_den',\n",
       " 'drift_380',\n",
       " 'mbb.60750_aper',\n",
       " 'mbb.60750',\n",
       " 'drift_381',\n",
       " 'mbb.60750_dex',\n",
       " 'drift_382',\n",
       " 'mba.60770_den',\n",
       " 'drift_383',\n",
       " 'mba.60770_aper',\n",
       " 'mba.60770',\n",
       " 'drift_384',\n",
       " 'mba.60770_dex',\n",
       " 'drift_385',\n",
       " 'mba.60790_den',\n",
       " 'drift_386',\n",
       " 'mba.60790_aper',\n",
       " 'mba.60790',\n",
       " 'drift_387',\n",
       " 'mba.60790_dex',\n",
       " 'drift_388',\n",
       " 'lof.60802_aper',\n",
       " 'lof.60802',\n",
       " 'drift_389',\n",
       " 'lsf.60805_aper',\n",
       " 'lsf.60805',\n",
       " 'drift_390',\n",
       " 'mdh.60807_aper',\n",
       " 'mdh.60807',\n",
       " 'drift_391',\n",
       " 'bph.60808_aper',\n",
       " 'bph.60808',\n",
       " 'drift_392',\n",
       " 'qf.60810_aper',\n",
       " 'qf.60810',\n",
       " 'drift_393',\n",
       " 'mba.60830_den',\n",
       " 'drift_394',\n",
       " 'mba.60830_aper',\n",
       " 'mba.60830',\n",
       " 'drift_395',\n",
       " 'mba.60830_dex',\n",
       " 'drift_396',\n",
       " 'mba.60850_den',\n",
       " 'drift_397',\n",
       " 'mba.60850_aper',\n",
       " 'mba.60850',\n",
       " 'drift_398',\n",
       " 'mba.60850_dex',\n",
       " ...)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "line.element_names  # Element names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "eef3746e",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<xtrack.beam_elements.elements.Marker at 0x7f2e5b925880>,\n",
       " <xtrack.beam_elements.elements.Marker at 0x7f2ed1d5a1c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2ed1d5a070>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8e1791f0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8e179400>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8e1794c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8e179580>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8e1793a0>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8e179700>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8e1797c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8e179880>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8e179940>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8e179a00>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8e179a60>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8e179c40>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8e179d30>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8e179d60>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8e179e80>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e5ace6070>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e5ace60a0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e5ace61c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e5ace6370>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e5ace6400>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e5ace64c0>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e5ace65b0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e5ace65e0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e5ace6700>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e5ace68b0>,\n",
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       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df26a30>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df26a60>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df26b80>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df26d30>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df26dc0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df26eb0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df26f40>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df25070>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df250a0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df251c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df25370>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df25400>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df25460>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8df25580>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df25730>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df25760>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8df25880>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df25a30>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df25a60>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df25b80>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df25d30>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df25dc0>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8df25e80>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df25f70>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df25fa0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df29100>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df292b0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df29340>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df29430>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df29460>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df29580>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df29730>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df297c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df298b0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df29940>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df29a30>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df29a60>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df29b80>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df29d30>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df29eb0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df29e20>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df29d90>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df2b070>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2b0a0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df2b1c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2b370>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df2b400>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2b4f0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df2b580>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df2b670>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2b6a0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df2b7c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2b970>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df2ba00>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2ba60>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df2bb80>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df2bd30>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2bd60>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df2be80>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2e070>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2e100>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8df2e1c0>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df2e2b0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2e2e0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df2e400>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2e5b0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df2e640>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df2e730>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2e760>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df2e880>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2ea30>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df2eac0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2ebb0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df2ec40>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df2ed30>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2ed60>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df2ee80>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2f070>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df2f100>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2f1f0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df2f280>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df2f370>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2f3a0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df2f4c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2f670>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df2f700>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2f7f0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df2f880>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df2f970>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2f9a0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df2fac0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2fc70>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df2fd00>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df2fd60>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8df2fe80>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df30070>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df300a0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df301c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df30370>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df30400>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8df304c0>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df305b0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df305e0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df30700>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df308b0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df30940>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df30a30>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df30a60>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df30b80>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df30d30>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df30dc0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df30eb0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df30f40>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df32070>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df320a0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df321c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df32370>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df32400>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df324f0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df32580>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df32670>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df326a0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df327c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df32970>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df32a00>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df32af0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df32b80>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df32c70>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df32ca0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df32dc0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df32f70>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df33040>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df330a0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df331c0>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df33370>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df333a0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df334c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df33670>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df33700>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8df338b0>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df33a30>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df33a60>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df33b80>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df33d30>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df33dc0>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df33eb0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df33ee0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df337c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df88eb0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df38040>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df381f0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df38280>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df38370>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df383a0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df384c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df38670>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df38700>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df387f0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df38880>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df38970>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df389a0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df38ac0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df38c70>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df38d00>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df38df0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df38e80>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df38f70>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df38fa0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df39100>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df392b0>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8df39340>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df39430>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df39460>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8df39580>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df39730>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df39760>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df39880>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df39a30>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df39ac0>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8df39b80>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df39c70>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df39ca0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df39dc0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df39f70>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df3a040>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df3a130>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df3a160>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df3a280>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df3a430>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df3a4c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df3a5b0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df3a640>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df3a730>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df3a760>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df3a880>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df3aa30>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df3aac0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df3abb0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df3ac40>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df3ad30>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df3ad60>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df3ae80>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df3d070>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df3d100>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df3d1f0>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df3d280>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df3d370>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df3d3a0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df3d4c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df3d670>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8df3d700>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df3d7f0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df3d820>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8df3d940>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df3daf0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df3db20>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df3dc40>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df3ddf0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df3de20>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df3df70>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df40130>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df401c0>,\n",
       " <xtrack.beam_elements.apertures.LimitEllipse at 0x7f2e8df40280>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df40370>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df403a0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df404c0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df40670>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df40700>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df407f0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df40820>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df40940>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df40af0>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df40b80>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df40c70>,\n",
       " <xtrack.beam_elements.apertures.LimitRect at 0x7f2e8df40d00>,\n",
       " <xtrack.beam_elements.elements.Multipole at 0x7f2e8df40df0>,\n",
       " <xtrack.beam_elements.elements.Drift at 0x7f2e8df40e20>,\n",
       " <xtrack.beam_elements.elements.DipoleEdge at 0x7f2e8df40f70>,\n",
       " ...)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "line.elements  # Element objects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7a98dc95",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<xtrack.beam_elements.elements.Multipole at 0x7f2e5ace9670>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "line['mbb.52070']  # A bending magnet"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e63febf",
   "metadata": {},
   "source": [
    "### Access the properties of individual elements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "540e4efc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'__class__': 'Multipole',\n",
       " 'order': 0,\n",
       " 'inv_factorial_order': 1.0,\n",
       " 'length': 6.26001860278045,\n",
       " 'hxl': 0.008445141542,\n",
       " 'hyl': 0.0,\n",
       " 'radiation_flag': 0,\n",
       " 'knl': array([0.00844514]),\n",
       " 'ksl': array([0.])}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "line['mbb.52070'].to_dict()  # We can view its properties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4bedef3a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'__class__': 'Multipole',\n",
       " 'order': 1,\n",
       " 'inv_factorial_order': 1.0,\n",
       " 'length': 3.085,\n",
       " 'hxl': 0.0,\n",
       " 'hyl': 0.0,\n",
       " 'radiation_flag': 0,\n",
       " 'knl': array([0.       , 0.0345839]),\n",
       " 'ksl': array([0., 0.])}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# A quadrupole\n",
    "line['qf.52010']\n",
    "line['qf.52010'].to_dict()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33e31567",
   "metadata": {},
   "source": [
    "### Twiss\n",
    "\n",
    "Compute orbit, optics and other quantities of interest."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "74b2f647",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute the twiss for the beamline\n",
    "line.particle_ref = xp.Particles(mass0=xp.PROTON_MASS_EV, p0c=26e9)\n",
    "tw = line.twiss()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "77c9cc7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "40b5640be2c6421d85e3a48c44801ed1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, \"$q_x$ = 20.15000 $q_y$ = 20.25000\\n$Q'_x$ = -1.32 $Q'_y$ = -0.72 $\\\\gamma_{tr}$ = 18.01\")"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, (spbet, spdx) = plt.subplots(nrows=2, ncols=1, sharex=True)\n",
    "spbet.plot(tw.s, tw.betx)\n",
    "spbet.plot(tw.s, tw.bety)\n",
    "spbet.set_ylim(bottom=0)\n",
    "spdx.plot(tw.s, tw.dx)\n",
    "spdx.plot(tw.s, tw.dy)\n",
    "\n",
    "spbet.set_ylabel(r'$\\beta_{x,y}$ [m]')\n",
    "spdx.set_ylabel(r\"$D_{x,y}$\")\n",
    "\n",
    "\n",
    "fig.suptitle(\n",
    "    r'$q_x$ = ' f'{tw[\"qx\"]:.5f}' r' $q_y$ = ' f'{tw[\"qy\"]:.5f}' '\\n'\n",
    "    r\"$Q'_x$ = \" f'{tw[\"dqx\"]:.2f}' r\" $Q'_y$ = \" f'{tw[\"dqy\"]:.2f}'\n",
    "    r' $\\gamma_{tr}$ = '  f'{1/np.sqrt(tw[\"momentum_compaction_factor\"]):.2f}'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "466e06e6",
   "metadata": {},
   "source": [
    "### Measure the tune"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "79e3412e",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_turns = 500\n",
    "\n",
    "p_co = tw.particle_on_co.copy()\n",
    "\n",
    "line.track(p_co, num_turns=num_turns, turn_by_turn_monitor=True)\n",
    "mon_co = line.record_last_track\n",
    "\n",
    "p1 = tw.particle_on_co.copy()\n",
    "p1.x += 0.1e-3\n",
    "p1.y += 0.2e-3\n",
    "line.track(p1, num_turns=num_turns, turn_by_turn_monitor=True)\n",
    "mon1 = line.record_last_track"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "aeea347b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2dd842933227457b844dabfb0da828a5",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'y [m]')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plot turn-by-turn data\n",
    "fig, (spx, spy) = plt.subplots(nrows=2, ncols=1, sharex=True)\n",
    "fig.suptitle('Turn-by-turn data')\n",
    "spx.plot(mon_co.x.T)\n",
    "spx.plot(mon1.x.T)\n",
    "spy.plot(mon_co.y.T)\n",
    "spy.plot(mon1.y.T)\n",
    "spy.set_xlabel('Turn')\n",
    "spx.set_ylabel('x [m]')\n",
    "spy.set_ylabel('y [m]')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4f02634b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b69000ac3fc0430c8072b252fa37167a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2e503b6220>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plot the transverse spectrum\n",
    "fig, (spx, spy) = plt.subplots(nrows=2, ncols=1, sharex=True)\n",
    "fig.suptitle('Transverse spectrum')\n",
    "freq_axis = np.fft.rfftfreq(n=num_turns)\n",
    "spx.plot(freq_axis, np.abs(np.fft.rfft(mon1.x[0, :])))\n",
    "spy.plot(freq_axis, np.abs(np.fft.rfft(mon1.y[0, :])))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eba8872c",
   "metadata": {},
   "source": [
    "Consistent with the twiss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7635c067",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20.15000024623154, 20.25000000092244)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tw.qx, tw.qy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f082fda7",
   "metadata": {},
   "source": [
    "### Survey"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3ffb58e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Run the survey\n",
    "sv = line.survey(element0=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7f77e0bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f37592252daf4e55b8330ab3e638e5e0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2e501ba070>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# See the whole ring\n",
    "fig, ax = plt.subplots()\n",
    "fig.suptitle('SPS Ring')\n",
    "ax.set_box_aspect(1)\n",
    "ax.plot(sv.Z, sv.X, label='x', linestyle='--', color='b')\n",
    "\n",
    "ax.plot(sv.Z, sv.X + tw.x, label='x', linestyle='-', color='b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9917a228",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "62.5702959144828"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.trapz(tw.betx, tw.s)/tw.circumference  # measure the simulated average beta function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "7f21ba4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "54.590569753176105"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tw.circumference/2/np.pi/tw.qx  # simplified estimate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a57939b7",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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