The quality of the proton beam produced by target normal sheath acceleration (TNSA) with high-power lasers can be significantly improved with the use of helical coils. While they showed promising results in terms of focusing, their performances in terms of the of cut-off energy and bunching stay limited due to the dispersive nature of helical coils. A new scheme of helical coil with a tube surrounding the helix is introduced, and the first numerical simulations and an analytical model show a possibility of a drastic reduction of the current pulse dispersion for the parameters of high-power-laser facilities. The helical coils with tube strongly increase bunching, creating two collimated narrow-band proton beams from a broad and divergent TNSA distribution. The analytical model provides scaling of proton parameters as a function of laser facility features.