  Recent observations found that electrons are accelerated to $\sim$10 GeV and
emit synchrotron hard X-rays in two magnetic white dwarfs (WDs), also known as
cataclysmic variables (CVs). In nova outbursts of WDs, multi-GeV gamma-rays
were detected inferring that protons are accelerated to 100 GeV or higher. In
recent optical surveys, the WD density is found to be higher near the Sun than
in the Galactic disk by a factor $\sim$2.5. The cosmic rays (CR) produced by
local CVs and novae will accumulate in the local bubble for $10^6$ - $10^7$
yrs. On these findings, we search for CRs from historic CVs and novae in the
observed CR spectra. We model the CR spectra at the heliopause as sums of
Galactic and local components based on observational data as much as possible.
The initial Galactic CR electron and proton spectra are deduced from the
gamma-ray emissivity, the local electron spectrum from the hard X-ray spectra
at the CVs, and the local proton spectrum inferred by gamma-ray spectrum at
novae. These spectral shapes are then expressed in a simple set of polynomial
functions of CR energy and regressively fitted until the high-energy ($>$100
GeV) CR spectra near Earth and the Voyager-1 spectra at the heliopause are
reproduced. We then extend the modeling to nuclear CR spectra and find that one
spectral shape fits all local nuclear CRs and the apparent hardening of the
nuclear CR spectra is caused by the roll-down of local nuclear spectra around
100 - 200 GeV. All local CR spectra populate in a limited energy band below 100
- 200 GeV and enhance gamma-ray emissivity below $\sim$10 GeV. Such an
enhancement is observed in the inner Galaxy, suggesting the CR fluxes from CVs
and novae are substantially higher there.
