beamparameters.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
 
"""
Scripts and functions to set the BeamParameters from known configurations
"""
 
from basf2 import B2FATAL, B2INFO
import math
import numpy as np
 
 
beamparameter_defaults = {
    "energyHER": 5.28,
    "energyLER": 5.28,
    "angleXHER": 0,
    "angleXLER": math.pi,
    "covHER": [0],
    "covLER": [0],
    "vertex": [0, 0, 0],
    "covVertex": [0]
}
 
 
beamparameter_presets = {
    "SuperKEKB": (None, {
        # beam energies in GeV
        "energyHER": 7.,
        "energyLER": 4.,
        # beam angles with respect to the z axis in radian, negative gets
        # converted into pi - |angle|
        "angleXHER": 0.0415,
        "angleXLER": -0.0415,
        # covariance matrices for the beam parametrized in
        # (E, theta_x, theta_y) = energy and horizontal and vertical angular
        # spread
        "covHER": np.array([0.00513]) ** 2,
        "covLER": np.array([0.002375]) ** 2,
        # bunch size in cm
        "bunchHER": np.array([10.2e-3, 59e-6, 6.0]) * 1e-1,
        "bunchLER": np.array([7.75e-3, 59e-6, 5.0]) * 1e-1,
    }),
    "Y1S": ("SuperKEKB", {  # m(Y1S) = 9.460 GeV
        "energyHER": 6.263,
        "energyLER": 3.579,
    }),
    "Y2S": ("SuperKEKB", {  # m(Y2S) = 10.023 GeV
        "energyHER": 6.635,
        "energyLER": 3.792,
    }),
    "Y3S": ("SuperKEKB", {  # m(Y3S) = 10.355 GeV
        "energyHER": 6.855,
        "energyLER": 3.917,
    }),
    "Y4S": ("SuperKEKB", {  # m(Y4S) = 10.579 GeV
        "energyHER": 7.004,
        "energyLER": 4.002,
    }),
    "Y5S": ("SuperKEKB", {  # m(Y5S) = 10.876 GeV
        "energyHER": 7.200,
        "energyLER": 4.114,
    }),
    "Y1S-off": ("Y1S", {  # m(Y1S) - 60 MeV = 9.400 GeV
        "energyHER": 6.223,
        "energyLER": 3.556,
    }),
    "Y2S-off": ("Y2S", {  # m(Y2S) - 60 MeV = 9.963 GeV
        "energyHER": 6.596,
        "energyLER": 3.769,
    }),
    "Y3S-off": ("Y3S", {  # m(Y3S) - 60 MeV = 10.295 GeV
        "energyHER": 6.816,
        "energyLER": 3.895,
    }),
    "Y4S-off": ("Y4S", {  # m(Y4S) - 60 MeV = 10.519 GeV
        "energyHER": 6.964,
        "energyLER": 3.979,
    }),
    "Y5S-off": ("Y5S", {  # m(Y5S) - 60 MeV = 10.816 GeV
        "energyHER": 7.160,
        "energyLER": 4.092,
    }),
    "Y1D1": ("SuperKEKB", {  # m(Y1D) = 10.152 GeV
        "energyHER": 6.720,
        "energyLER": 3.840,
    }),
    "Y2D1": ("SuperKEKB", {  # m(Y2D) = 10.425 GeV
        "energyHER": 6.901,
        "energyLER": 3.944,
    }),
    "Y6S": ("SuperKEKB", {  # m(Y6S) = 11.020 GeV
        "energyHER": 7.295,
        "energyLER": 4.169,
    }),
    "Yb10775": ("SuperKEKB", {  # m(Yb10775) = 10.775 GeV
        "energyHER": 7.133,
        "energyLER": 4.076,
    }),
    "KEKB-Belle": (None, {
        "energyHER": 7.998213,
        "energyLER": 3.499218,
        "angleXHER": 0.022,
    }),
    "LEP1": (None, {
        "energyHER": 45.6,
        "energyLER": 45.6,
    }),
    "DAPHNE": (None, {
        "energyHER": 1.02 / 2.,
        "energyLER": 1.02 / 2.,
    }),
}
 
 
def __get_4vector(energy, angle):
    """Calculate an 4vector for electron/positron from energy and angle"""
    import ROOT
    m = 0.511e-3
    pz = (energy ** 2 - m ** 2) ** .5
    v = ROOT.Math.PxPyPzEVector(0, 0, pz, energy)
    if angle < 0:
        angle = math.pi + angle
    rotationY = ROOT.Math.RotationY(angle)
    v = rotationY(v)
    return v
 
 
def rot_matrix_y(angle):
    """Return rotation matrix for a rotation of angle around the y-axis"""
    c = math.cos(angle)
    s = math.sin(angle)
    return np.matrix([(c, 0, s), (0, 1, 0), (-s, 0, c)])
 
 
def cov_matrix(beamsize, angle):
    """Return the covariance matrix for the given bunch size and angle with
    respect to the z axis"""
    if angle < 0:
        angle = math.pi + angle
    rot = rot_matrix_y(angle)
    cov = np.matrix(np.diag(beamsize ** 2))
    return rot * cov * rot.T
 
 
def calculate_beamspot(pos_her, pos_ler, size_her, size_ler, angle_her, angle_ler):
    """
    Function to calculate position and covariance matrix of the beamspot.
 
    This function calculates the mean position and the covariance matrix for the
    beamspot from the bunch positions, bunch sizes and the angles of the beam
    with respect to the z-axis. It assumes normal distributed bunch densities and
    multiplies the PDFs for the two bunches to get a resulting beamspot
 
    negative angles are interpreted as "math.pi - abs(angle)"
 
    Args:
        pos_her (list): mean position of the HER bunch (in cm)
        pos_ler (list): mean position of the LER bunch (in cm)
        size_her (list): HER bunch size in cm
        size_ler (list): LER bunch size in cm
        angle_her (float): angle between HER direction and z-axis
        angle_her (float): angle between LER direction and z-axis
 
    Returns:
        pos (array): array (x, y, z) with the spot center in cm
        cov (matrix): covariance matrix of the beam spot
    """
 
    cov_her = cov_matrix(size_her, angle_her)
    cov_ler = cov_matrix(size_ler, angle_ler)
    # calculate the inverse of the sum of the two covariance matrices
    cov_sum_i = (cov_her + cov_ler).I
    # and use it to calculate the product of the two gaussian distributions,
    # covariance and mean
    cov_spot = cov_her * cov_sum_i * cov_ler
    beampos_spot = np.array(
        cov_ler * cov_sum_i * np.matrix(pos_her).T +
        cov_her * cov_sum_i * np.matrix(pos_ler).T
    ).T[0]
    return beampos_spot, cov_spot
 
 
def add_beamparameters(path, name, E_cms=None, **argk):
    """Add BeamParameter module to a given path
 
    Args:
        path (basf2.Path instance): path to add the module to
        name (str): name of the beamparameter settings to use
        E_cms (float): center of mass energy. If not None the beamenergies will
            be scaled accordingly to achieve E_cms
 
    Additional keyword arguments will be passed directly to the module as parameters.
    """
    # calculate all the parameter values from the preset
    values = calculate_beamparameters(name, E_cms)
    # add a BeamParametes module to the path
    module = path.add_module("BeamParameters")
    module.set_name("BeamParameters:%s" % name)
    # finally, set all parameters and return the module
    module.param(values)
    # and override parameters with any additional keyword arguments
    module.param(argk)
    return module
 
 
def calculate_beamparameters(name, E_cms=None):
    """Get/calculate the necessary beamparameter values from the given preset name,
    optionally scale it to achieve the given cms energy
 
    Args:
        name (str): name of the beamparameter settings to use
        E_cms (float): center of mass energy. If not None the beamenergies will
            be scaled accordingly to achieve E_cms
    """
    if name not in beamparameter_presets:
        B2FATAL("Unknown beamparameter preset: '%s', use one of %s" %
                (name, ", ".join(sorted(beamparameter_presets.keys()))))
        return None
 
    # copy the defaults
    values = beamparameter_defaults.copy()
 
    # collect all the values from the preset by also looping over the
    preset = {}
 
    def collect_values(preset, name):
        parent, values = beamparameter_presets[name]
        if parent is not None:
            collect_values(preset, parent)
        preset.update(values)
 
    collect_values(preset, name)
 
    # and update with the preset
    for k in values.keys():
        if k in preset:
            if isinstance(preset[k], np.ndarray):
                values[k] = list(preset[k].flat)
            else:
                values[k] = preset[k]
 
    # if we have bunch sizes we want to compute the vertex covariance from them
    if "bunchHER" in preset and "bunchLER" in preset:
        her_size = preset["bunchHER"]
        ler_size = preset["bunchLER"]
        her_angle = values["angleXHER"]
        ler_angle = values["angleXLER"]
        _, cov = calculate_beamspot(
            [0, 0, 0], [0, 0, 0], her_size, ler_size, her_angle, ler_angle
        )
        values["covVertex"] = list(cov.flat)
 
    if E_cms is not None:
        ler = __get_4vector(values["energyLER"], values["angleXLER"])
        her = __get_4vector(values["energyHER"], values["angleXHER"])
        mass = (her + ler).M()
        scale = E_cms / mass
        B2INFO("Scaling beam energies by %g to obtain E_cms = %g GeV" % (scale, E_cms))
        values["energyHER"] *= scale
        values["energyLER"] *= scale
 
    return values
 
 
if __name__ == "__main__":
    # if called directly we will
    # 1. calculate the beamspot for the SuperKEKB preset and display it if possible
    # 2. calculate beam energies for Y1S - Y5S and offresonance
    np.set_printoptions(precision=3)
 
    # calculate beamspot for SuperKEKB for testing
    
    values = beamparameter_presets["SuperKEKB"][1]
    beampos_spot, cov_spot = calculate_beamspot(
        [0, 0, 0], [0, 0, 0],
        values["bunchHER"], values["bunchLER"],
        values["angleXHER"], values["angleXLER"],
    )
    print("Beamspot position:")
    print(beampos_spot)
    print("Beamspot covariance:")
    print(cov_spot)
    print("Beamspot dimensions (in mm, axes in arbitary order):")
    print(np.linalg.eig(cov_spot)[0] ** .5 * 10)
 
    # see if we can plot it
    try:
        from matplotlib import pyplot as pl
        
        cov_her = cov_matrix(values["bunchHER"], values["angleXHER"])
        
        cov_ler = cov_matrix(values["bunchLER"], values["angleXLER"])
        
        points_her = np.random.multivariate_normal([0, 0, 0], cov_her, 1000)
        
        points_ler = np.random.multivariate_normal([0, 0, 0], cov_ler, 1000)
        
        points_spot = np.random.multivariate_normal(beampos_spot, cov_spot, 1000)
        pl.scatter(points_her[:, 2], points_her[:, 0], s=5, marker=".", c="b", edgecolors="None", label="HER")
        pl.scatter(points_ler[:, 2], points_ler[:, 0], s=5, marker=".", c="r", edgecolors="None", label="LER")
        pl.scatter(points_spot[:, 2], points_spot[:, 0], s=5, marker=".", c="g", edgecolors="None", label="spot")
        pl.legend()
        pl.xlabel("z / cm")
        pl.ylabel("x / cm")
        pl.tight_layout()
        pl.show()
    except ImportError:
        pass
 
    
    eher = values["energyHER"]
    
    eler = values["energyLER"]
    
    aher = values["angleXHER"]
    
    aler = values["angleXLER"]
 
    # calculate beam energies for Y1S - Y4S by scaling them from the nominal
    # beam energies for the SuperKEKB preset
    
    ler = __get_4vector(eher, aher)
    
    her = __get_4vector(eler, aler)
    
    mass = (her + ler).M()
    print("Nominal CMS Energy: ", mass)
 
    
    targets = {
        "Y1S": 9460.30e-3,
        "Y2S": 10023.26e-3,
        "Y3S": 10355.2e-3,
        "Y4S": 10579.4e-3,
        "Y5S": 10876e-3
    }
    for name, energy in sorted(targets.items()):
        
        scale = energy / mass
        print("""\
            "%s": ("SuperKEKB", {  # m(%s) = %.3f GeV
                "energyHER": %.3f,
                "energyLER": %.3f,
            }),""" % (name, name, energy, eher * scale, eler * scale))
 
    for name, energy in sorted(targets.items()):
        
        scale = (energy - 60e-3) / mass
        print("""\
            "%s-off": ("%s", {  # m(%s) - 60 MeV = %.3f GeV
                "energyHER": %.3f,
                "energyLER": %.3f,
            }),""" % (name, name, name, energy - 60e-3, eher * scale, eler * scale))