transverse dynamics 41
EXERCISES
2.1 Chapter materials review.
Define the region of parameters where a pair of thin
quadrupoles will focus the beam in both planes.
2.2 Chapter materials review.
Prove the Eq. 2.39, which defines the stability of a FODO
beamline, geometrically, using the analogy with a traditional
geometrical optics.
2.3 Chapter materials review.
A parallel proton beam of E=200 MeV enters a beamline. It is
necessary to focus this beam into a point at a 3 m distance
from the entrance. Estimate the necessary parameters of a
quadrupole system (gradients, lengths) that can perform this
task.
2.4 Mini-project.
Consider the same proton beam as in the previous exercise,
as well as the same focusing requirements. Assume that the
focusing is performed by a continuous, cylindrical electron
beam. Estimate the necessary electron density which can perform the focusing task. Select electron beam energy, determine the electron current and discuss and select an optimal
design of the electron beam system, as well as its feasibility.
2.5 Analyze inventions or discoveries using TRIZ and AS-TRIZ.
Analyze and describe scientific or technical inventions described in this chapter in terms of the TRIZ and AS-TRIZ approaches, identifying a contradiction and an inventive principle that were used (could have been used) for these inventions.
2.6 Developing AS-TRIZ parameters and inventive principles.
Based on what you already know about accelerator science,
discuss and suggest the possible additional parameters for
the AS-TRIZ contradiction matrix, as well as the possible additional AS-TRIZ inventive principles.
EXERCISES
2.1 Chapter materials review.
Define the region of parameters where a pair of thin
quadrupoles will focus the beam in both planes.
2.2 Chapter materials review.
Prove the Eq. 2.39, which defines the stability of a FODO
beamline, geometrically, using the analogy with a traditional
geometrical optics.
2.3 Chapter materials review.
A parallel proton beam of E=200 MeV enters a beamline. It is
necessary to focus this beam into a point at a 3 m distance
from the entrance. Estimate the necessary parameters of a
quadrupole system (gradients, lengths) that can perform this
task.
2.4 Mini-project.
Consider the same proton beam as in the previous exercise,
as well as the same focusing requirements. Assume that the
focusing is performed by a continuous, cylindrical electron
beam. Estimate the necessary electron density which can perform the focusing task. Select electron beam energy, determine the electron current and discuss and select an optimal
design of the electron beam system, as well as its feasibility.
2.5 Analyze inventions or discoveries using TRIZ and AS-TRIZ.
Analyze and describe scientific or technical inventions described in this chapter in terms of the TRIZ and AS-TRIZ approaches, identifying a contradiction and an inventive principle that were used (could have been used) for these inventions.
2.6 Developing AS-TRIZ parameters and inventive principles.
Based on what you already know about accelerator science,
discuss and suggest the possible additional parameters for
the AS-TRIZ contradiction matrix, as well as the possible additional AS-TRIZ inventive principles.