J un 2 00 0 1 Polarized Protons in HERA
Polarized proton beams at HERA can currently only be produced by extracting a beam from a polarized source and then accelerating it in the three synchrotrons at DESY. In this paper, the processes which can depolarize a proton beam in circular accelerators are explained, devices which could avoid this depolarization in the DESY accelerator chain are described, and specific problems which become important at the high energies of HERA are mentioned. At HERA’s high energies, spin motion cannot be accurately described with the isolated resonance model which has been successfully used for lower energy rings. To illustrate the principles of more accurate simulations, the invariant spin field is introduced to describe the equilibrium polarization state of a beam and the changes during acceleration. It will be shown how linearized spin motion leads to a computationally quick approximation for the invariant spin field and how to amend this with more time consuming but accurate non-perturbative computations. Analysis with these techniques has allowed us to establish optimal Siberian Snake schemes for HERA.
Tracking algorithm for the stable spin polarization field in storage rings using stroboscopic averaging.
Polarized protons have never been accelerated to more than about $25$GeV. To achieve polarized proton beams in RHIC (250GeV), HERA (820GeV), and the TEVATRON (900GeV), ideas and techniques new to accelerator physics are needed. In this publication we will stress an important aspect of very high energy polarized proton beams, namely the fact that the equilibrium polarization direction can vary substantially across the beam in the interaction region of a high energy experiment when no countermeasure is taken. Such a divergence of the polarization direction would not only diminish the average polarization available to the particle physics experiment, but it would also make the polarization involved in each collision analyzed in a detector strongly dependent on the phase space position of the interacting particle. In order to analyze and compensate this effect, methods for computing the equilibrium polarization direction are needed. In this paper we introduce the method of stroboscopic averaging, which computes this direction in a very efficient way. Since only tracking data is needed, our method can be implemented easily in existing spin tracking programs. Several examples demonstrate the importance of the spin divergence and the applicability of stroboscopic averaging.
THE ATLANTIC SLAVE TRADE AND COLONIALISM: REASONS FOR AFRICA’S UNDERDEVELOPMENT?
It is probably an understatement to assert that Africa, the world’s second largest continent, is underdeveloped compared with other continents. Two major exogenous factors often cited for Africa’s development crisis are the so called ‘dual historical injustices’ – the Atlantic slave trade and colonialism. It is often pointed out that while the former almost completely arrested and retarded Africa’s demographical growth for more than three centuries, evoked a perennial state of acrimony and warfare and created a tense and unprecedented atmosphere of insecurity which hindered economic activities and stifled local entrepreneurship and technological drive and dislocated Africa’s socio-economic and political structures and institutions; the latter tied African countries to the apron strings of western imperial powers thereby rendering the pre-conditions necessary for socio-economic and political transformation unachievable. This paper contends that while the history of Africa’s underdevelopment may be traceable to the Atlantic slave trade and colonialism, African leaders had made enormous contributions to the continent’s underdevelopment and backwardness. The paper concludes that irresponsible and irresponsive leadership, vampirism and prodigality, corruption, lack of respect for democratic ideals, insecurity, endemic civil wars, nepotism, etc are the fundamental causes of Africa’s underdevelopment.