I mean in manufacturing a bicycle we know how to "ensemble" a bicycle, what actions and "assembly of parts". So what steps are needed for make a photon?
Also is there a limit on how many photons for an emisor can make?
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Photons, and in fact all other elementary particles, are not assembled. They exist. We don't know how, or why, they simply do.
Photons are the quanta of the electromagnetic field - in quantum field theory, we associate to the classical electromagnetic field particles called photons. For a technical account if how this (roughly) works, read my answer to "The concept of particle in QFT".
Between quantum fields, there are so called interactions, which are commonly represented by Feynman diagrams. The electromagnetic field interacts with all electrically charges fields, making it possible for every charged particle to emit a photon if it "spends" enough energy to do so. The creation of a photon is, in the simplest case, just a straight line representing a charged particle from which a photon line simply starts anywhere. The standard example for photon creations are transitions in atoms: Here, an electron "jumps" from a higher to a lower orbit, thereby lowering its energy, and emits a photon that carries exactly the amount of energy lost.
There is no detail to the creation of a photon, or any other fundamental particle. If it is an allowed interaction in the underlying quantum field theory, it can happen. We simply don't know anything more, and we don't know if there even is anything more to know.
Whenever one makes light, one makes zillions of photons, so the way to make photons is the way to generate light: burning wood etc, striking stones, make wires incandescent, as in electric bulbs, etc, fusing nuclei as in the sun and stars and maybe more ways. It is much easier to make zillions of photons.
How one photon is made takes us to the realm of particle physics, similar to the way of finding one atom, the microcosm, and the experiments become much more demanding and expensive :).
A photon can be made in the lab by exciting an atom's electrons to higher orbitals and waiting for the atom to relax by emitting a photon , as in burning and sparks.
It can be made by accelerating and decelerating electrons , in cathode ray tubes where we get x-ray photons.
It can be made by nuclear reactions, fission and fusion.
It can be made by high energy particles hitting each other in the LHC and generating elementary particles, among which are gamma rays.
I don't think you can understand how a photon is made without knowing what a photon is, and to understand what a photon is requires understanding quantum field theory - specifically quantum electrodynamics.
Quantum field theory is a very odd way of looking at the world, but it works and gives predictions that agree with experiment. In quantum field theory every particle has an associated quantum field that fills all of spacetime. So for example there is an electron field. We can add or remove energy from the electron quantum field, but because the field is quantised we can only add or remove energy in discrete quanta of 511 keV. You might recognise that energy of 511 keV, because it's the energy of a single electron. If we add 511 keV of energy to the electron quantum field then that energy appears as an electron, so by adding energy top the quantum field we create a particle. Likewise we can take energy out of the quantum field and the result is that a particle disappears.
This is how the large hadron collider can create particles like the Higgs from the collision of protons. The enormous kinetic energy of colliding quarks can be transferred into the Higgs quantum field where it appears as a Higgs particle. All the hundreds of particles that typically emerge from an LHC collision were created by transferring energy into their associated quantum fields.
The point of all this is that there is a photon quantum field. If we transfer energy into the photon field then it appears as a photon i.e. we have created a photon. And that's what you asked about.
The question is then how do we transfer energy into the photon field to make photons. Well energy is transferred between quantum fields, and the photon field can exchange energy with any other quantum field with which it has a non-zero coupling. Quantum field theory tells us how and why that energy transfer can occur to create photons. I think photons can only interact through the electromagnetic force - I say I think because I believe there is some debate about whether photons can scatter off neutrinos via a weak interaction. Anyhow, any field that represents a charged particle can couple to the photon field and transfer energy to it.