A dipole amplifier for electric dipole moments, axion-like particles and
  a dense dark matter hairs detector
  A tool that can constrain, in minutes, beyond-the-standard-model parameters
like electric dipole moments (EDM) down to a lower-bound
$d_\text{e}^{\cal{N}}<10^{-37}\text{e}\cdot\text{cm}$ in bulk materials, or the
coupling of axion-like particles (ALP) to photons down to
$|G_{a\gamma\gamma}|<10^{-16}$~GeV$^{-1}$, is described. Best limits are
$d^n_e<3\cdot10^{-26}\text{e}\cdot\text{cm}$ for neutron EDM and
$|G_{a\gamma\gamma}|<6.6\cdot10^{-11}$~GeV$^{-1}$. The {\it dipole amplifier}
is built from a superconducting loop immersed in a toroidal magnetic field,
$\vec{B}$. When nuclear magnetic moments in the London penetration depth align
with $\vec{B}$, the bulk magnetization is always accompanied by an EDM-induced
bulk electric field $\vec{E}\propto\vec{B}$ that generates detectable
oscillatory supercurrents with a characteristic frequency
$\omega_{\text{D}}\propto d_\text{e}^{\cal{N}}$. Cold dark matter (CDM) ALP are
formally similar where $\omega_\text{D}\propto
|G_{a\gamma\gamma}|\sqrt{n_a/(2m_a)}$ with $m_a$ the ALP mass and $n_a$ its
number density. A space probe traversing a dark matter hair with a dipole
amplifier is sensitive enough to detect ALP density variations if
$|G_{a\gamma\gamma}|\sqrt{n_h/(2m_a)}>4.9\cdot10^{-27}$ where $n_h$ is the ALP
number density in the hair.
