Abstract: In this study, we examine multiple algebras and
algebraic structures derived from them and by stating a theory on
multiple algebras; we will show that the theory of multiple algebras
is a natural extension of the theory of universal algebras. Also, we
will treat equivalence relations on multiple algebras, for which the
quotient constructed modulo them is a universal algebra and will
study the basic relation and the fundamental algebra in question.
In this study, by stating the characteristic theorem of multiple
algebras, we show that the theory of multiple algebras is a natural
extension of the theory of universal algebras.
Abstract: Three-dimensional simulation of harmonic up
generation in free electron laser amplifier operating simultaneously
with a cold and relativistic electron beam is presented in steady-state
regime where the slippage of the electromagnetic wave with respect
to the electron beam is ignored. By using slowly varying envelope
approximation and applying the source-dependent expansion to wave
equations, electromagnetic fields are represented in terms of the
Hermit Gaussian modes which are well suited for the planar wiggler
configuration. The electron dynamics is described by the fully threedimensional
Lorentz force equation in presence of the realistic planar
magnetostatic wiggler and electromagnetic fields. A set of coupled
nonlinear first-order differential equations is derived and solved
numerically. The fundamental and third harmonic radiation of the
beam is considered. In addition to uniform beam, prebunched
electron beam has also been studied. For this effect of sinusoidal
distribution of entry times for the electron beam on the evolution of
radiation is compared with uniform distribution. It is shown that
prebunching reduces the saturation length substantially. For
efficiency enhancement the wiggler is set to decrease linearly when
the radiation of the third harmonic saturates. The optimum starting
point of tapering and the slope of radiation in the amplitude of
wiggler are found by successive run of the code.
Abstract: THEOS is the first earth observation spacecraft of Thailand which was launched on the 1st October 2008 and is currently operated by GISTDA. The transfer phase has been performed by Astrium Flight Dynamics team leading to a hand over to GISTDA teams starting mid-October 2008. The THEOS spacecraft-s orbit is LEO and has the same repetitivity (14+5/26) as the SPOT spacecraft, i.e. the same altitude of 822 km but it has a different mean local solar time (LST). Ground track maintenance manoeuvres are performed to maintain the ground track within a predefined control band around the reference ground track and the band is ±40 km for THEOS spacecraft. This paper presents the first ground track maintenance manoeuvre of THEOS spacecraft and the detailed results. In addition, it also includes one and a half year of operation as seen by GISTDA operators. It finally describes the foreseenable activities for the next orbit control manoeuvre (OCM) preparation.