Initial Pencil Research Articles

Two-dimensional frequency scanning from a metasurface-based Fabry–Pérot resonant cavity

A spatial angular filtering metasurface is introduced into a Fabry–Pérot (FP) resonant cavity design for the frequency scanning performance in this paper. More specifically, asymmetrical unit cells printed on the metasurface enable the radiation energy to move in different directions as the frequency changes, and the released emissions, meanwhile, are split into dual-beams from the initial pencil beam. We continue to implement a patch array to provide excitation with the aim of achieving scanned beams in another dimension, and the proposed design ultimately demonstrates a two-dimensional dual-beam scanning performance with 42° and 9° scanning angles respectively in two dimensions of the coordinate system over a frequency range from 10.50 GHz–11.25 GHz. The proposed technique, by integrating a spatial angular filtering metasurface with a patch array feed to generate steerable beams, should offer an efficient way to fulfill FP resonant cavities with reconfigurable radiation.

Redesigning a Reaction Control Thruster for Metal-Based Additive Manufacturing: A Case Study in Design for Additive Manufacturing

Prior research has shown that powder-bed fusion (PBF) additive manufacturing (AM) can be used to make functional, end-use components from powdered metallic alloys, such as Inconel® 718 superalloy. However, these end-use components and products are often based on designs developed for more traditional subtractive manufacturing processes and do not take advantage of the unique design freedoms afforded by AM. In this paper, we present a case study involving the redesign of NASA’s existing “pencil” thruster used for spacecraft attitude control. The initial pencil thruster was designed for and manufactured using traditional subtractive methods. The main focus in this paper is to (a) identify the need for and use of both opportunistic and restrictive design for additive manufacturing (DfAM) concepts and considerations in redesigning the thruster for fabrication with PBF AM and (b) compare the resulting DfAM thruster with a parallel development effort redesigning the original thruster to be manufactured more effectively using subtractive manufacturing processes. The results from this case study show how developing end-use AM components using specific DfAM guidelines can significantly reduce manufacturing time and costs while enabling new and novel design geometries.

SU-GG-T-98: Pencil Beam for Electron Intraoperative Radiotherapy. Early Results from Profile and Percentage Depth Dose Modelling

Purpose: To evaluate the feasibility and the accuracy of pencil beam modelling for electron intraoperative radiotherapy (IORT). Methods and materials: A complete set of dose measurements in water have been performed. They have been made with different source‐to‐applicator‐end distance, bevel angle, applicator size and beam energy. Dose measurements in air have also been made with one applicator size and bevel 0° to obtain initial pencil beam angular spread and fluence intensity profile. An Elekta Precise and a Varian 21 EX linacs have been used. Modelling has been carried out by Tecnicas Radiofisicas (Zaragoza, Spain) adapting a modified Hogstrom's pencil beam implemented in TPS PCRT3D for external Radiotherapy.Results: Different profiles have been obtained according to different machine and applicator design. Lack of accuracy has been kept within 2% or 3% in most of the reference profiles modelled. Nevertheless, it rose to more than 5% for little applicator size, 30° and 45° bevel angle and high energy when modelling Varian beams. Discrepancies for Elekta modelling data have appeared when increasing bevel angle. Additional difficulties have been found when modelling beam edges for little applicators. Besides, percentage depth dose have been modelled for both machines and discrepancies are under investigation. Conclusions: Pencil beam is able to model IORT beams in water for dose delivery calculation. A trade‐off between accuracy and linac time expense should be achieved. Thus, accuracy could be increased if taking extra dedicated data for each combination of energy and applicator size. Then, an improvement of modelling at beam edges should be expected, especially for large bevel angles. The authors expect that further research will lead to calculate absorbed dose in an IORT patient, turning an IORT virtual simulator developed by GMV (Madrid, Spain), Radiance, into a treatment planning system. Supported by grant PSE‐300000‐2009‐5. Ministerio de Ciencia e Innovacion. Spanish Government.

SU-FF-T-271: Influence of Initial Pencil Beam Parameters On Large Non-Applicator Electron Field Profiles Calculated Using Monte Carlo Methods

Purpose: To investigate the influence of the initial pencil beam width on large non-applicator electron field profiles calculated using the BEAMnrc/EGSnrc Monte Carlo code. For a Varian 2100C linear accelerator, significant discrepancies of up to 10% in the shoulder of the profile were found between measured and calculated profiles for 40×40 cm2 electron fields collimated using x-ray jaws alone, when using the standard electron spot size of 1.5 mm. A small angular variance of the electron pencil-beam at the x-ray target would be equivalent to increasing the electron pencil-beam spot size at the primary scattering foil, which would be expected to affect the electron fluence profile exiting the linear accelerator. Method and Materials: Cross-beam profiles at the depth of maximum central-axis dose were measured and calculated for electron beams with a field size of 40×40 cm2 collimated by the x-ray jaws without an electron applicator. The electron spot size at the position of the x-ray target was modeled as a mono-energetic mono-directional Gaussian with a full-width half-maximum (FWHM) that varied from 1.5 to 5 mm. For each energy, measured and calculated profiles were compared to determine the optimal FWHM. Results: Adjusting the FWHM of the source greatly affected the shoulder of the calculated off-axis profiles, reducing discrepancies to ±4%. The optimal FWHM ranged 2.5 to 4.5 mm and was energy dependent. Assuming that the correct spot size at the x-ray target is 1.5 mm, this is equivalent to an angular spread at the x-ray target of 8.8 to 20.9 mrad. Conclusion: The angular spread of the electron pencil-beam at the x-ray target is significant and varies with energy, mostly influencing the shoulders of large non-applicator electron field profiles. The effect of the initial angular spread on other dosimetric data will be the subject of future investigations.

The mass angular scattering power method for determining the kinetic energies of clinical electron beams

The method is based on the measurement in air of the spatial spread of a pencil electron beam which is produced from the broad clinical electron beam. As predicted by the Fermi-Eyges theory, the dose distribution measured in air on a plane, perpendicular to the incident direction of the initial pencil electron beam, is Gaussian. The square of its spatial spread is related to the mass angular scattering power which in turn is related to the kinetic energy of the electron beam. The measured spatial spread may thus be used to determine the mass angular scattering power, which is then used to determine the kinetic energy of the electron beam from the known relationship between mass angular scattering power and kinetic energy. Energies obtained with the mass angular scattering power method agree with those obtained with the electron range method.

Energy dependent 4-dimensional multiple scattering distributions

A complete analytic solution in Fourier space is presented of the four dimensional small angle, multiple scattering distribution MSD in angle and space, produced by an energy dependent single scattering cross section from an initial pencil beam of heavy particles. Independently, simple integrals are derived for the central moments of the energy dependent MSD in the continuous-slowing-down approximation. The distributions of the projections t and x of the scattering angle and displacement into a plane through the axis of propagation are evaluated numerically for a truncated Rutherford scattering cross section using a fast Fourier transform. The resulting MSDs for a wide range of particles, initial and final momenta, and scattering materials are found to be approximately represented by one-dimensional set of standard distributions symmetrized by a linear transformation in t− x-space.

Spectral problem for polynomial matrix pencils. 2

For an arbitrary polynomial pencil of matrices Ai of dimensions m×n one presents an algorithm for the computation of the eigenvalues of the regular kernel of the pencil. The algorithm allows to construct a regular pencil having the same eigenvalues as the regular kernel of the initial pencil or (in the case of a dead end termination) allows to pass from the initial pencil to a pencil of smaller dimensions whose regular kernel has the same eigenvalues as the initial pencil. The problem is solved by reducing the obtained pencil to a linear one. For solving the problem in the case of a linear pencil one considers algorithms for pencils of full column rank as well as for completely singular pencils.

A general approach to reducing a regular linear pencil to a pencil of quasitriangular form

A general approach to constructing the algorithms for solving a spectral problem for a regular pencil A − λB of matrices by reducing it to a pencil of quasitriangular form with diagonal boxes which have eigenvalues equal in absolute value to that of the initial pencil is discussed. A theoretical justification of the approach proposed, and examples of constructing algorithms are given.

Calculational methods for estimating skin dose from electrons in Co-60 gamma-ray beams.

Several methods have been employed to calculate the relative contribution to skin dose due to scattered electrons in Co-60 gamma-ray beams. Either the Klein-Nishina differential scattering probability is employed to determine the number and initial energy of electrons scattered into the direction of a detector, or a Gaussian approximation is used to specify the surface distribution of initial pencil electron beams created by parallel or diverging photon fields. Results of these calculations are compared with experimental data. In addition, that fraction of relative surface dose resulting from photon interactions in air alone is estimated and compared with data extrapolated from measurements at large source-surface distance (SSD). The contribution to surface dose from electrons generated in air is 50% or more of the total skin dose for SSDs greater than 80 cm.

Solution of the partial eigenvalue problem for a regular matrix pencilD(?) =A ? ?B

One presents the ALGOL procedures which implement the algorithm for the determination of the group of smallest (greatest) eigenvalues and their corresponding eigenvectors for a matrix pencil where A and B are real square matrices of simple structure. From the initial pencil one constructs a matrix C, whose eigenvalues are taken as the initial approximations to the eigenvalues from the group of the smallest (greatest) eigenvalues of the pencil. The refinement of the eigen-values is performed on the basis of the theory of perturbations. Then one determines the eigen-vectors and one computes the infinite norm of the residual. One gives ALGOL programs and test examples.

TheAB-algorithm and its properties

One presents a new algorithm, called the -algorithm, for solving the generalized eigenvalue problem Ax=λBx, where det (A—λB) ≠ 0, relative to A. The algorithm is iterative, it is based on the application of plane rotations and allows us to pass from the initial problem to the solving of a similar problem having simpler matrices, whose eigenvalues can be easily computed and coincide with the eigenvalues of the initial problem. Thus, if all the eigenvalues of the initial problem are distinct, then the application of the -algorithm leads to the computation of the eigenvalues of a pencil with triangular matrices. In the case of an arbitrary initial pencil A—λB, the problem reduces to solving the eigenvalue problem for a pencil of quasitriangular form. One proves the convergence of the algorithm. One establishes its properties which in many respects are similar with the properties of the known algorithms QR and QZ, the first of which solves the usual eigenvalue problem while the second one solves the generalized problem of the above-mentioned form.

Analysis of singular matrix pencils

One considers the spectral problem for a singular pencil D(λ)=A + λB of matrices A and B (A and B are rectangular matrices or det D(λ)≡0). One represents an algorithm which allows us to find the reducing subspaces for D(λ) and with their aid to reduce the dimension of the initial pencil, by isolating from it the zero block, the blocks corresponding to the right and left polynomial solutions of the equations (A+λB)x(λ)=0 and y(λ)(A+λB)=0, respectively, as well as the block corresponding to the regular kernel of the pencil D(λ). The algorithm is based on the application of the normalized process which uses the numerically stable elementary orthogonal transformations (the matrices of plane rotations or reflections).

On the reflection of transverse waves from a cold plasma

It is demonstrated that a pencil of low frequency waves incident from vacuum onto a cold plasma, at angles other than normal incidence, gives rise to a reflected pencil of rays which is not in the plane of incidence of the initial pencil, in general. The importance of this planar shift for plasma diagnostics is pointed out.