![Page 1: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/1.jpg)
ºHoliday Inn Pachuca 2016 Pachuca, Hidalgo, 101116
Optimized Monochromatization
for Direct Higgs Production at the FCCe+e-
L(λ)Supported in part by the European Commission under Capacities 7th Framework Programme project EuCARD-2, grant agreement 312453.
![Page 2: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/2.jpg)
Motivation
![Page 3: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/3.jpg)
Motivations
• Questions still unanswered about Higgs boson properties
• Post-LHC era requirements
• Upcoming beamstrahlung effects
• FCC proposal opportunity
• Monochromatization for high center-of-mass energy resolution
![Page 4: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/4.jpg)
Objectives
![Page 5: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/5.jpg)
Objectives
• Present a review of the field of accelerator physics and future proposals
• Characterize beamstrahlung at the FCCe+e-
• Obtain the self-consistent energy spread and self-consistent emittance
• Optimize the IP parameters to produce opposite dispersion
• Develop a monochromatization scheme for the FCCe+e-
• Describe the modification to the lattice design and the final focusing system
![Page 6: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/6.jpg)
Accelerator Physics
![Page 7: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/7.jpg)
Storage Ring A Qualitative Description
• Particles are injected into a vacuum chamber until the beam is stored.
• The guide field provides focusing capabilities driving particles toward the ideal designed.
• Stored particles loss energy by synchrotron radiation, compensated in average by the RFS.
• The periodic accelerating field collects the particles into circulating bunches.
• Energy loss by synchrotron radiation leads into damping of all oscillation amplitudes.
• Amplitude excitation occurs as an effect of the quantum nature of radiation.
• A balance between radiation damping and quantum excitation is reached.
![Page 8: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/8.jpg)
Monochromatization principle A “simple explanation”
![Page 9: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/9.jpg)
Monochromatization principle A “simple explanation”
![Page 10: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/10.jpg)
Monochromatization principle In Optical Terms
• A special arrangement of elements or modification of the available ones is required
• In the context of this proposal, exploration of the current FCCee design is needed
• In literature, insertions to implement this idea is known as monochromator
![Page 11: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/11.jpg)
Lattice Design Courant-Snyder Theory
Hill Differential Equation
Ansatz
Courant-Snyder Parameters
Courant-Snyder Invariant
![Page 12: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/12.jpg)
Lattice Design Dispersion
Off-Momentum Particles
Relative Momentum Deviation
Momentum Contribution
Dispersion Function
Dispersion Contribution
Approximations
Dipole Contribution
![Page 13: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/13.jpg)
Lattice Design Lattice Parameters
General ContributionDispersion Contribution
Dispersion Function
Area of the Ellipse
Size of the Distribution
Normalized Emittance
![Page 14: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/14.jpg)
Synchrotron Radiation
![Page 15: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/15.jpg)
Synchrotron radiation Energy Deviation Effects
Off-Energy ContributionOff-Energy Particles
Radius of Curvature
Equation of Motion for Off-Energy Particles
Ultrarelativistic Limit
![Page 16: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/16.jpg)
Synchrotron radiation Off-Energy Equation of Motion
Off-Energy ContributionDispersion Equation
D
FQ
DQ
BM
![Page 17: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/17.jpg)
Synchrotron radiation Dilation Factor
Length Increment
Dilation Factor
Ratio Orbit Length Revolution Time
Relative Revolution Time Increment
![Page 18: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/18.jpg)
Synchrotron radiation Energy Oscillations
Azimuthal Displacement
Time Displacement
Time Displacement Evolution
RF Energy Supply
Energy Change
Energy Evolution
![Page 19: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/19.jpg)
Synchrotron radiation Energy Oscillations
Time Displacement Evolution
If
Time displacement
In Complex Notation
![Page 20: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/20.jpg)
Synchrotron radiation Quantum Radiation Effects
Instantaneous Power
Spectrum Function
Critical Frequency
Photon Spectrum Rate
![Page 21: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/21.jpg)
Synchrotron radiation Quantum Radiation Effects
Excitation Term
Statistical Properties
![Page 22: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/22.jpg)
Synchrotron radiation Quantum Radiation Effects
Energy Deviation Oscillation
Photon Emission
New Amplitude
Probable Amplitude Change
For Sinusoidal Energy Oscillation
Probable Amplitude Squared
![Page 23: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/23.jpg)
Beamstrahlung
![Page 24: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/24.jpg)
Beamstrahlung Sokolov-Ternov Theory
Lorentz Invariant
Quantum Spectrum Formula
Classical Spectrum Formula
![Page 25: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/25.jpg)
Beamstrahlung Sokolov-Ternov Theory
Photon Emission Rate
Average Emitted Photons
Relative Energy Loss
Statistical PropertiesClassical Formula
![Page 26: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/26.jpg)
Beamstrahlung Sokolov-Ternov Theory
Photon Emission Rate
Statistical Properties
![Page 27: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/27.jpg)
Beamstrahlung Self-Consistant Energy Spread
Excitation Term
Total Energy Spread
Bunch LengthDispersion Invariant
![Page 28: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/28.jpg)
Beamstrahlung Self-Consitant Equations
Monochromatization Baseline
Self-Consistent Equations
![Page 29: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/29.jpg)
Monochromatization
![Page 30: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/30.jpg)
Beam Parameters Distributions
Transverse Displacement
Phase Space Distribution
Average at the IP
Average over distribution
![Page 31: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/31.jpg)
Without Monochromatization Colliding Beams
Collision Energy Spread
Beam Energy Spread
Function of radius and Jϵ
Typical Options
Monochromatization
![Page 32: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/32.jpg)
Without Monochromatization Standard Monochromatization
Standard Monochromatization
Baseline Scheme
Standard Monochromatization
![Page 33: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/33.jpg)
Monochromatization factor λ(Dx *, βx* = 0.25 m)
Standard Monochromatization
![Page 34: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/34.jpg)
Monochromatization factor λ(Dx * = 0.11 m, βx*)
Standard Monochromatization
![Page 35: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/35.jpg)
Beamstrahlung Effects on Monochromatization
Self-Consistent Equations
Baseline Monochromatization
Statistical Properties
![Page 36: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/36.jpg)
Baseline monochromatization
Width of standard model Higgs 4-5 MeV requires λ ≥ 10 Nb = 3.3x1010 nb = 25760 βy* = 2 mm
Monochromatization Factor
: λ = 9.2, L = 1 x 1035 cm-2s-1
![Page 37: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/37.jpg)
Baseline monochromatization
Width of standard model Higgs 4-5 MeV requires λ ≥ 10 Nb = 3.3x1010 nb = 25760 βy* = 2 mm
: λ = 9.2, L = 1 x 1035 cm-2s-1
Luminosity contours
![Page 38: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/38.jpg)
Failed “pushed” monochromatization
Pushed monochromatization:
Nb = 8.5x1010
nb = 10000
βy* = 1 mm
: λ = 2.3, L = 7.5 x 1035 cm-2s-1
Monochromatization Factor
![Page 39: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/39.jpg)
Failed “pushed” monochromatization
Pushed monochromatization:
Nb = 8.5x1010
nb = 10000
βy* = 1 mm
Luminosity contours
: λ = 2.3, L = 7.5 x 1035 cm-2s-1
![Page 40: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/40.jpg)
Optimized Monochromatization Luminosity_max and λ
: λ0 = 10.17321
Monochromatization FactorS = [ 0.1 , 3 ], T = [ 0.1 , 3 ]
β0x = 1.0 m, β0y = 1.0 mm
D0x = 0.22 m
N0b = 3.3x1010, n0b = 25760
βx = β0x * S2, Dx * = D0x * S
Nb = N0b / T, nb = n0b * T
![Page 41: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/41.jpg)
Optimized Monochromatization Luminosity_max and λ
: λ0 = 10.17321, L ~ 1 x 1036 cm-2s-1
Luminosity contoursS = [ 0.1 , 3 ], T = [ 0.1 , 3 ]
β0x = 1.0 m, β0y = 1.0 mm
D0x = 0.22 m
N0b = 3.3x1010, n0b = 25760
βx = β0x * S2, Dx * = D0x * S
Nb = N0b / T, nb = n0b * T
![Page 42: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/42.jpg)
Lmax vs λ
Optimized Monochromatization Luminosity_max and λ
: λ0 = 10.17321, L ~ 1 x 1036 cm-2s-1
S = [ 0.1 , 3 ], T = [ 0.1 , 3 ]
β0x = 1.0 m, β0y = 1.0 mm
D0x = 0.22 m
N0b = 3.3x1010, n0b = 25760
βx = β0x * S2, Dx * = D0x * S
Nb = N0b / T, nb = n0b * T
![Page 43: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/43.jpg)
Luminosity_max and λ
Monochromatization FactorS = [ 0.1 , 3 ], T = [ 0.1 , 3 ]
β0x = 1.0 m, β0y = 1.0 mm
D0x = 0.22 m
N0b = 3.3x1010, n0b = 25760
βx = β0x * S2, Dx * = D0x * S
Nb = N0b / T, nb = n0b * T
: λ = 5.07, β = 1.96 m, Dx = 0.308 m, L = 3.736 x 1035 cm-2s-1
![Page 44: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/44.jpg)
Conclusions
![Page 45: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/45.jpg)
• Monochromatization scheme can be implemented.
• Beamstrahlung effects may be controlled.
• Simulation supports predictions.
• Lattice designed is still in progress and the required
modification should be possible.
• Theory confirmation could be achieved at the FCCe+e-
: λ = 5.07, β = 1.96 m, Dx = 0.308 m, L = 3.736 x 1035 cm-2s-1
![Page 46: Supported in part by the European Commission under Capacities … · 2016-11-11 · º Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116 Optimized Monochromatization for Direct Higgs](https://reader033.vdocuments.net/reader033/viewer/2022042119/5e97cee5999c240e9d628429/html5/thumbnails/46.jpg)
Ing. M. Alan Valdivia G. [email protected]
Holiday Inn Pachuca 2016 Pachuca, Hidalgo, 101116
Optimized Monochromatization
for Direct Higgs Production at the FCCe+e-
L(λ)Supported in part by the European Commission under Capacities 7th Framework Programme project EuCARD-2, grant agreement 312453.