Investigation of Propagation Characteristics of Twisted Hollow Waveguides for Particle Accelerator Applications

A new class of accelerating structures employing a uniformly twisted waveguide is investigated. Twisted waveguides of various cross-sectional geometries are considered and analyzed. It is shown that such a twisted waveguide can support waves that travel at a speed slower than the speed of light c. The slow-wave properties of twisted structures are of interest because these slow-wave electromagnetic fields can be used in applications such as electron traveling wave tubes and linear particle accelerators. Since there is no exact closed form solution for the electromagnetic fields within a twisted waveguide or cavity, several previously proposed approximate methods are examined, and more efficient approaches are developed. It is found that the existing perturbation theory methods yield adequate results for slowly twisted structures; however, our efforts here are geared toward analyzing rapidly twisted structures using modified finite difference methods specially suited for twisted structures. Although the method can handle general twisted structures, three particular cross sections are selected as representative cases for careful analysis. First, a slowly twisted rectangular cavity is analyzed as a reference case. This is because its shape is simple and perturbation theory already gives a good approximate solution for such slow twists rates. Secondly, a symmetrically notched circular cross section is investigated, since its longitudinal cross section is comparable to the well known disk-loaded cavity (used in many practical accelerator designs, including SLAC). Finally, a dumbbell shaped cross section is analyzed because of its similarity to the well-known TESLA-type accelerating cavity, which is of great importance because of its wide acceptance as a superconducting cavity. To validate the results of the developed theory and our extensive simulations, the newly developed numerical models are compared to commercial codes. Also, several prototypes are developed employing the three basic shapes discussed previously. Bench measurements are performed on the prototype cavities to evaluate dispersion by measuring the field distribution along these cavities. The measurement results are compared to the simulations and theoretical results, and good agreement is shown. Once validated, the developed models are used to design twisted accelerating structures with specific phase velocities and good accelerating performance

Spatially distributed computational modeling of a nonlinear vibrating string

Värähtelevän kielen epälineaarinen käyttäytyminen saa monissa kielisoittimissa aikaan soittimelle luonteenomaisen ja helposti tunnistettavan äänen. Laadukkaan kielisoitinsynteesin vuoksi onkin tärkeää, että nykyaikaiset äänisynteesimenetelmät ottavat huomioon myös kielten epälineaarisuudet. Tässä diplomityössä esitellään kaksi uutta synteesimenetelmää, jotka fysikaalisen mallinnuksen avulla simuloivat epälineaarisia näpättyjä kieliä paikkajakautuneesti, keskittyen jännitysmodulaation tuottamiin epälineaarisuuksiin. Toinen menetelmistä käyttää hajautettuja murtoviivesuotimia digitaalisen aaltojohtomallin viivesilmukan pituuden ajonaikaisessa virittämisessä, kun taas toinen hyödyntää murtoviivesuotimia äärelliseen erotukseen pohjautuvan mallin aikaresoluution muuttamisessa ajon aikana. Jännitysmodulaation suuruus arvioidaan kummankin mallin tapauksessa jokaisella aika-askeleella kielen pidentymästä. Molempien mallien simulaatiotulokset esitellään ja niitä verrataan toisiinsa sekä myös mitattuihin arvoihin. Epälineaarisen aaltojohtomallin avulla on toteutettu reaaliaikainen kantelemalli.Nonlinearities in string instruments are responsible for several interesting acoustical features, resulting in characteristic and easily recognizable tones. For this reason, modern synthesis models have to be capable of modeling this nonlinear behavior, when high quality results are desired. This thesis presents two novel physical modeling algorithms for simulating the tension modulation nonlinearity in plucked strings in a spatially distributed manner. The first method uses fractional delay filters within a digital waveguide structure, allowing the length of the string to be modulated during run time. The second method uses a nonlinear finite difference approach, where the string state is approximated between sampling instants also using fractional delay filters, thus allowing run-time modulation of the temporal sampling location. The magnitude of the tension modulation is evaluated from the elongation of the string at every time step in both cases. Simulation results of the two models are presented and compared. Real-time sound synthesis of the kantele, a traditional Finnish plucked-string instrument with strong effect of tension modulation, has been implemented using the nonlinear digital waveguide algorithm