All of the high-energy physics colliders built in recent decades have collided one beam of particles with a second beam traveling in the opposite direction. For example, the Large Hadron Collider at CERN sends particles of opposite charges around a ring, with one beam traveling clockwise and the second traveling counterclockwise. Technically it is much more difficult to get the two beams to collide with one another in this way as compared to just having one beam slamming into a stationary target, yet this still how colliders are built. Consider the following two situations. In the first picture, (the modern collider design), two equal mass m particles collide, each with total energy Ecollider, to produce some exotic new particle of mass M, at rest. Conservation of energy says that 2Ecollider = Mc^2. On the other hand, in the second picture (the fixed-target design), a particle of mass m with energy Efixed hits an identical mass particle at rest, producing the same exotic new particle (with mass M) as in the previous process: Calculate the value of Efixed + mc^2 - the total energy required in the fixed target design - and compare it to 2Ecollider - the initial energy in the collider design. When you have an answer, find what energy the fixed target accelerator would need to replace a 50 GeV-on-50 GeV electron-positron collider. Is it 100 GeV?
All of the high-energy physics colliders built in recent decades have collided one beam of particles with a second beam traveling in the opposite direction. For example, the Large Hadron Collider at CERN sends particles of opposite charges around a ring, with one beam traveling clockwise and the second traveling counterclockwise. Technically it is much more difficult to get the two beams to collide with one another in this way as compared to just having one beam slamming into a stationary target, yet this still how colliders are built.
Consider the following two situations. In the first picture, (the modern collider design), two equal mass m particles collide, each with total energy Ecollider, to produce some exotic new particle of mass M, at rest. Conservation of energy says that 2Ecollider = Mc^2. On the other hand, in the second picture (the fixed-target design), a particle of mass m with energy Efixed hits an identical mass particle at rest, producing the same exotic new particle (with mass M) as in the previous process:
Calculate the value of Efixed + mc^2 - the total energy required in the fixed target design - and compare it to 2Ecollider - the initial energy in the collider design. When you have an answer, find what energy the fixed target accelerator would need to replace a 50 GeV-on-50 GeV electron-positron collider. Is it 100 GeV?
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