The Future Circular Collider for hadrons (FCC-hh) is a proposed high-energy frontier particle accelerator, which would be built in a new ~100 km circumference tunnel and would enable proton-proton collisions at a centre-of-mass energy of 100 TeV. The baseline injection energy is 3.3 TeV. The FCC-hh will require a fast injection kicker system that is highly reliable and does not limit accelerator performance. To achieve low ripple and fast rise and fall time field pulses, the injection system will use ferrite loaded transmission line type magnets. The FCC-hh will operate at high beam intensity: hence, the beam coupling impedance will be an issue. The problems are twofold: longitudinal and transverse impedance may drive beam instabilities, while the real part of the longitudinal impedance gives rise to beam induced heating. The power deposition in the kicker magnet can cause a temperature increase of the ferrite yoke above its Curie point: this would affect the ability to inject beam. For a high beam current and a short bunch length, a high power deposition would occur in unshielded FCC-hh injection kicker magnets: hence, a beam screen is a critical feature. Amongst the most challenging requirements for the beam screen are: low broadband beam coupling impedance, fast field rise and fall time, low field ripple during the flat-top field and good high voltage behaviour. In this thesis, we propose and develop a novel concept of a spiral beam screen. The fundamental advantage of the new design, in comparison to the conventional straight screen conductors used for example in the LHC injection kickers, is a significant reduction of the maximum voltage induced on the conductors, thus a greatly reduced probability of an electrical breakdown of the beam screen. Also, the spiral screen design allows a reduction of the maximum transverse beam coupling impedance of the kicker system. Both the conventional and spiral designs are studied from a theoretical, a numerical, and an experimental point of view. Important new contributions brought to the field of kicker magnets include: real-time data analysis of the output waveform of the LHC kicker magnet to ensure the ferrite yoke is below its Curie point; a new CST and PSpice model of the FCC-hh injection kicker magnets; proposal and development of new calculation and measurement methods for determining power loss distribution in the ferrite of a kicker magnet; and novel measurements of the electromagnetic properties of ferrites as a function of frequency and temperature.