Anna Heffernan | University of Florida (original) (raw)
Address: Gainesville, U.S.
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Papers by Anna Heffernan
We consider the interplanetary trajectory design problem posed by the 8th edition of the Global T... more We consider the interplanetary trajectory design problem posed by the 8th edition of the Global Trajectory Optimization Competition and present the end-to-end strategy developed by the team ACT-ISAS (a collaboration between the European Space Agency's Advanced Concepts Team and JAXA's Institute of Space and Astronautical Science). The resulting interplanetary trajectory won 1st place in the competition, achieving a final mission value of J = 146.33 [Mkm]. Several new algorithms were developed in this context but have an interest that go beyond the particular problem considered, thus, they are discussed in some detail. These include the Moon-targeting technique, allowing one to target a Moon encounter from a low Earth orbit; the 1-k and 2-k fly-by targeting techniques, enabling one to design resonant fly-bys while ensuring a targeted future formation plane; the distributed low-thrust targeting technique, admitting one to control the spacecraft formation plane at 1,000,000 [km]; and the low-thrust optimization technique, permitting one to enforce the formation plane's orientations as path constraints.
Phys. Rev. D 89, 024030 (2014), Jan 22, 2014
In a previous paper, we computed expressions for the Detweiler-Whiting singular field of point s... more In a previous paper, we computed expressions for the Detweiler-Whiting singular field of point
scalar, electromagnetic and gravitational charges following a geodesic of the Schwarzschild spacetime.
We now extend this to the case of equatorial orbits in Kerr spacetime, using coordinate and covariant
approaches to compute expansions of the singular field in scalar, electromagnetic and gravitational
cases. As an application, we give the calculation of previously unknown mode-sum regularization
parameters. We also propose a new application of high-order approximations to the singular field,
showing how they may be used to compute m-mode regularization parameters for use in the m-mode
effective source approach to self-force calculations
Phys. Rev. D 82, 104023 (2012), Nov 7, 2012
The self-field of a charged particle has a singular component that diverges at the particle. We ... more The self-field of a charged particle has a singular component that diverges at the particle. We
use both coordinate and covariant approaches to compute an expansion of this singular field for
particles in generic geodesic orbits about a Schwarzschild black hole for scalar, electromagnetic and
gravitational cases. We check that both approaches yield identical results and give, as an application,
the calculation of previously unknown mode-sum regularisation parameters.
In the so-called mode-sum regularization approach to self-force calculations, each mode of the
retarded field is finite, while their sum diverges. The sum may be rendered finite and convergent
by the subtraction of appropriate regularization parameters. Higher order parameters lead to faster
convergence in the mode-sum. To demonstrate the significant benefit that they yield, we use our
newly derived parameters to calculate a highly accurate value of Fr = 0.000013784482575667959(3)
for the self-force on a scalar particle in a circular orbit around a Schwarzschild black hole.
Finally, as a second example application of our high-order expansions, we compute high-order
expressions for use in the effective source approach to self-force calculations.
We consider the interplanetary trajectory design problem posed by the 8th edition of the Global T... more We consider the interplanetary trajectory design problem posed by the 8th edition of the Global Trajectory Optimization Competition and present the end-to-end strategy developed by the team ACT-ISAS (a collaboration between the European Space Agency's Advanced Concepts Team and JAXA's Institute of Space and Astronautical Science). The resulting interplanetary trajectory won 1st place in the competition, achieving a final mission value of J = 146.33 [Mkm]. Several new algorithms were developed in this context but have an interest that go beyond the particular problem considered, thus, they are discussed in some detail. These include the Moon-targeting technique, allowing one to target a Moon encounter from a low Earth orbit; the 1-k and 2-k fly-by targeting techniques, enabling one to design resonant fly-bys while ensuring a targeted future formation plane; the distributed low-thrust targeting technique, admitting one to control the spacecraft formation plane at 1,000,000 [km]; and the low-thrust optimization technique, permitting one to enforce the formation plane's orientations as path constraints.
Phys. Rev. D 89, 024030 (2014), Jan 22, 2014
In a previous paper, we computed expressions for the Detweiler-Whiting singular field of point s... more In a previous paper, we computed expressions for the Detweiler-Whiting singular field of point
scalar, electromagnetic and gravitational charges following a geodesic of the Schwarzschild spacetime.
We now extend this to the case of equatorial orbits in Kerr spacetime, using coordinate and covariant
approaches to compute expansions of the singular field in scalar, electromagnetic and gravitational
cases. As an application, we give the calculation of previously unknown mode-sum regularization
parameters. We also propose a new application of high-order approximations to the singular field,
showing how they may be used to compute m-mode regularization parameters for use in the m-mode
effective source approach to self-force calculations
Phys. Rev. D 82, 104023 (2012), Nov 7, 2012
The self-field of a charged particle has a singular component that diverges at the particle. We ... more The self-field of a charged particle has a singular component that diverges at the particle. We
use both coordinate and covariant approaches to compute an expansion of this singular field for
particles in generic geodesic orbits about a Schwarzschild black hole for scalar, electromagnetic and
gravitational cases. We check that both approaches yield identical results and give, as an application,
the calculation of previously unknown mode-sum regularisation parameters.
In the so-called mode-sum regularization approach to self-force calculations, each mode of the
retarded field is finite, while their sum diverges. The sum may be rendered finite and convergent
by the subtraction of appropriate regularization parameters. Higher order parameters lead to faster
convergence in the mode-sum. To demonstrate the significant benefit that they yield, we use our
newly derived parameters to calculate a highly accurate value of Fr = 0.000013784482575667959(3)
for the self-force on a scalar particle in a circular orbit around a Schwarzschild black hole.
Finally, as a second example application of our high-order expansions, we compute high-order
expressions for use in the effective source approach to self-force calculations.